Practice calculating the area of composite figures using given dimensions.
Worksheet titled "Area of Composite Figures" with 15 geometric shapes, each labeled with dimensions, designed for calculating area in square units.
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Step-by-step solution for: Area of Composite Figures Worksheets 2024
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Step-by-step solution for: Area of Composite Figures Worksheets 2024
This image is a worksheet titled "Area of Composite Figures." It contains 20 different composite shapes, each with labeled side lengths. The task is to calculate the area of each shape, with the understanding that the drawings are not to scale and the answers should be in square units.
To solve this, I will need to break down each composite figure into simpler geometric shapes (like rectangles, squares, triangles, and sometimes semicircles) whose areas I can calculate using standard formulas. Then, I will sum or subtract these areas as needed to find the total area of the composite figure.
I'll start by solving the first problem in the top-left corner to demonstrate the method.
The first shape is an L-shape. I can calculate its area by dividing it into two rectangles.
- Rectangle 1 (Top): This rectangle has a length of 8 units and a height of 3 units.
- Area = $8 \times 3 = 24$ square units.
- Rectangle 2 (Bottom): This rectangle has a length of 5 units and a height of 4 units.
- Area = $5 \times 4 = 20$ square units.
- Total Area: Add the areas of the two rectangles.
- Total Area = $24 + 20 = 44$ square units.
---
Now, I will proceed to solve all 20 problems systematically. To ensure accuracy, I will tackle them one by one.
This is another L-shape. I can divide it into two rectangles.
- Rectangle 1 (Top): Length = 7 units, Height = 3 units.
- Area = $7 \times 3 = 21$ square units.
- Rectangle 2 (Right): Length = 2 units, Height = 6 units.
- Area = $2 \times 6 = 12$ square units.
- Total Area: $21 + 12 = 33$ square units.
---
This shape resembles a T. I can divide it into two rectangles.
- Rectangle 1 (Bottom): Length = 12 units, Height = 5 units.
- Area = $12 \times 5 = 60$ square units.
- Rectangle 2 (Top): Length = 4 units, Height = 3 units.
- Area = $4 \times 3 = 12$ square units.
- Total Area: $60 + 12 = 72$ square units.
---
This shape is a rectangle with a semicircle on top.
- Rectangle: Length = 4 units, Height = 8 units.
- Area = $4 \times 8 = 32$ square units.
- Semicircle: The diameter is 4 units, so the radius is 2 units.
- Area of a full circle = $\pi r^2 = \pi \times 2^2 = 4\pi$.
- Area of semicircle = $\frac{1}{2} \times 4\pi = 2\pi$ square units.
- Total Area: $32 + 2\pi$ square units.
---
This is a rectangle with a smaller rectangle cut out from the bottom.
- Large Rectangle: Length = 10 units, Height = 8 units.
- Area = $10 \times 8 = 80$ square units.
- Cut-out Rectangle: Length = 2 units, Height = 2 units.
- Area = $2 \times 2 = 4$ square units.
- Total Area: $80 - 4 = 76$ square units.
---
This shape is a trapezoid on top of a rectangle.
- Rectangle: Length = 14 units, Height = 4 units.
- Area = $14 \times 4 = 56$ square units.
- Trapezoid: The two parallel sides are 14 units and 6 units, and the height is 8 units (since the total height is 12 and the rectangle is 4).
- Area = $\frac{1}{2} \times (14 + 6) \times 8 = \frac{1}{2} \times 20 \times 8 = 80$ square units.
- Total Area: $56 + 80 = 136$ square units.
---
This is a complex L-shape. I can divide it into two rectangles.
- Rectangle 1 (Bottom): Length = 12 units, Height = 10 units.
- Area = $12 \times 10 = 120$ square units.
- Rectangle 2 (Top): Length = 7 units, Height = 10 units (since the total height is 20 and the bottom rectangle is 10).
- Area = $7 \times 10 = 70$ square units.
- Total Area: $120 + 70 = 190$ square units.
---
This is a step-like shape. I can divide it into three rectangles.
- Rectangle 1 (Bottom): Length = 6 units, Height = 3 units.
- Area = $6 \times 3 = 18$ square units.
- Rectangle 2 (Middle): Length = 6 units, Height = 6 units.
- Area = $6 \times 6 = 36$ square units.
- Rectangle 3 (Top): Length = 6 units, Height = 3 units.
- Area = $6 \times 3 = 18$ square units.
- Total Area: $18 + 36 + 18 = 72$ square units.
---
This is a combination of a triangle and a rectangle.
- Rectangle: Length = 8 units, Height = 10 units.
- Area = $8 \times 10 = 80$ square units.
- Triangle: Base = 18 units, Height = 4 units.
- Area = $\frac{1}{2} \times 18 \times 4 = 36$ square units.
- Total Area: $80 + 36 = 116$ square units.
---
This is an arrow shape. I can divide it into a triangle and a rectangle.
- Rectangle: Length = 6 units, Height = 4 units.
- Area = $6 \times 4 = 24$ square units.
- Triangle: Base = 6 units, Height = 10 units.
- Area = $\frac{1}{2} \times 6 \times 10 = 30$ square units.
- Total Area: $24 + 30 = 54$ square units.
---
This is a complex L-shape. I can divide it into two rectangles.
- Rectangle 1 (Left): Length = 16 units, Height = 22 units.
- Area = $16 \times 22 = 352$ square units.
- Rectangle 2 (Right): Length = 8 units, Height = 15 units.
- Area = $8 \times 15 = 120$ square units.
- Total Area: $352 + 120 = 472$ square units.
---
This is an L-shape. I can divide it into two rectangles.
- Rectangle 1 (Vertical): Length = 16 units, Height = 16 units.
- Area = $16 \times 16 = 256$ square units.
- Rectangle 2 (Horizontal): Length = 12 units, Height = 3 units.
- Area = $12 \times 3 = 36$ square units.
- Total Area: $256 + 36 = 292$ square units.
---
This is an L-shape. I can divide it into two rectangles.
- Rectangle 1 (Vertical): Length = 8 units, Height = 30 units.
- Area = $8 \times 30 = 240$ square units.
- Rectangle 2 (Horizontal): Length = 34 units, Height = 15 units.
- Area = $34 \times 15 = 510$ square units.
- Total Area: $240 + 510 = 750$ square units.
---
This shape is a rectangle with a semicircle on the left.
- Rectangle: Length = 22 units, Height = 10 units.
- Area = $22 \times 10 = 220$ square units.
- Semicircle: The diameter is 10 units, so the radius is 5 units.
- Area of a full circle = $\pi r^2 = \pi \times 5^2 = 25\pi$.
- Area of semicircle = $\frac{1}{2} \times 25\pi = 12.5\pi$ square units.
- Total Area: $220 + 12.5\pi$ square units.
---
This is a complex shape. I can divide it into two rectangles.
- Rectangle 1 (Bottom): Length = 20 units, Height = 15 units.
- Area = $20 \times 15 = 300$ square units.
- Rectangle 2 (Top): Length = 16 units, Height = 5 units.
- Area = $16 \times 5 = 80$ square units.
- Total Area: $300 + 80 = 380$ square units.
---
This is an L-shape. I can divide it into two rectangles.
- Rectangle 1 (Vertical): Length = 9 units, Height = 12 units.
- Area = $9 \times 12 = 108$ square units.
- Rectangle 2 (Horizontal): Length = 18 units, Height = 7 units.
- Area = $18 \times 7 = 126$ square units.
- Total Area: $108 + 126 = 234$ square units.
---
This is a complex shape. I can divide it into three rectangles.
- Rectangle 1 (Top): Length = 32 units, Height = 14 units.
- Area = $32 \times 14 = 448$ square units.
- Rectangle 2 (Left): Length = 11 units, Height = 9 units.
- Area = $11 \times 9 = 99$ square units.
- Rectangle 3 (Right): Length = 16 units, Height = 9 units.
- Area = $16 \times 9 = 144$ square units.
- Total Area: $448 + 99 + 144 = 691$ square units.
---
This is a complex shape. I can divide it into three rectangles.
- Rectangle 1 (Top): Length = 16 units, Height = 18 units.
- Area = $16 \times 18 = 288$ square units.
- Rectangle 2 (Middle): Length = 34 units, Height = 18 units.
- Area = $34 \times 18 = 612$ square units.
- Rectangle 3 (Bottom): Length = 16 units, Height = 18 units.
- Area = $16 \times 18 = 288$ square units.
- Total Area: $288 + 612 + 288 = 1188$ square units.
---
This is a rectangle with a smaller rectangle cut out from the top.
- Large Rectangle: Length = 30 units, Height = 20 units.
- Area = $30 \times 20 = 600$ square units.
- Cut-out Rectangle: Length = 18 units, Height = 6 units.
- Area = $18 \times 6 = 108$ square units.
- Total Area: $600 - 108 = 492$ square units.
---
This is a combination of a triangle and a rectangle.
- Rectangle: Length = 10 units, Height = 28 units.
- Area = $10 \times 28 = 280$ square units.
- Triangle: Base = 24 units, Height = 12 units.
- Area = $\frac{1}{2} \times 24 \times 12 = 144$ square units.
- Total Area: $280 + 144 = 424$ square units.
---
Here are the areas for all 20 composite figures:
1. 44 square units
2. 33 square units
3. 72 square units
4. $32 + 2\pi$ square units
5. 76 square units
6. 136 square units
7. 190 square units
8. 72 square units
9. 116 square units
10. 54 square units
11. 472 square units
12. 292 square units
13. 750 square units
14. $220 + 12.5\pi$ square units
15. 380 square units
16. 234 square units
17. 691 square units
18. 1188 square units
19. 492 square units
20. 424 square units
To solve this, I will need to break down each composite figure into simpler geometric shapes (like rectangles, squares, triangles, and sometimes semicircles) whose areas I can calculate using standard formulas. Then, I will sum or subtract these areas as needed to find the total area of the composite figure.
I'll start by solving the first problem in the top-left corner to demonstrate the method.
Problem 1 (Top-Left)
The first shape is an L-shape. I can calculate its area by dividing it into two rectangles.
- Rectangle 1 (Top): This rectangle has a length of 8 units and a height of 3 units.
- Area = $8 \times 3 = 24$ square units.
- Rectangle 2 (Bottom): This rectangle has a length of 5 units and a height of 4 units.
- Area = $5 \times 4 = 20$ square units.
- Total Area: Add the areas of the two rectangles.
- Total Area = $24 + 20 = 44$ square units.
---
Now, I will proceed to solve all 20 problems systematically. To ensure accuracy, I will tackle them one by one.
Problem 2 (Top Row, Second from Left)
This is another L-shape. I can divide it into two rectangles.
- Rectangle 1 (Top): Length = 7 units, Height = 3 units.
- Area = $7 \times 3 = 21$ square units.
- Rectangle 2 (Right): Length = 2 units, Height = 6 units.
- Area = $2 \times 6 = 12$ square units.
- Total Area: $21 + 12 = 33$ square units.
---
Problem 3 (Top Row, Third from Left)
This shape resembles a T. I can divide it into two rectangles.
- Rectangle 1 (Bottom): Length = 12 units, Height = 5 units.
- Area = $12 \times 5 = 60$ square units.
- Rectangle 2 (Top): Length = 4 units, Height = 3 units.
- Area = $4 \times 3 = 12$ square units.
- Total Area: $60 + 12 = 72$ square units.
---
Problem 4 (Top Row, Fourth from Left)
This shape is a rectangle with a semicircle on top.
- Rectangle: Length = 4 units, Height = 8 units.
- Area = $4 \times 8 = 32$ square units.
- Semicircle: The diameter is 4 units, so the radius is 2 units.
- Area of a full circle = $\pi r^2 = \pi \times 2^2 = 4\pi$.
- Area of semicircle = $\frac{1}{2} \times 4\pi = 2\pi$ square units.
- Total Area: $32 + 2\pi$ square units.
---
Problem 5 (Second Row, First from Left)
This is a rectangle with a smaller rectangle cut out from the bottom.
- Large Rectangle: Length = 10 units, Height = 8 units.
- Area = $10 \times 8 = 80$ square units.
- Cut-out Rectangle: Length = 2 units, Height = 2 units.
- Area = $2 \times 2 = 4$ square units.
- Total Area: $80 - 4 = 76$ square units.
---
Problem 6 (Second Row, Second from Left)
This shape is a trapezoid on top of a rectangle.
- Rectangle: Length = 14 units, Height = 4 units.
- Area = $14 \times 4 = 56$ square units.
- Trapezoid: The two parallel sides are 14 units and 6 units, and the height is 8 units (since the total height is 12 and the rectangle is 4).
- Area = $\frac{1}{2} \times (14 + 6) \times 8 = \frac{1}{2} \times 20 \times 8 = 80$ square units.
- Total Area: $56 + 80 = 136$ square units.
---
Problem 7 (Second Row, Third from Left)
This is a complex L-shape. I can divide it into two rectangles.
- Rectangle 1 (Bottom): Length = 12 units, Height = 10 units.
- Area = $12 \times 10 = 120$ square units.
- Rectangle 2 (Top): Length = 7 units, Height = 10 units (since the total height is 20 and the bottom rectangle is 10).
- Area = $7 \times 10 = 70$ square units.
- Total Area: $120 + 70 = 190$ square units.
---
Problem 8 (Second Row, Fourth from Left)
This is a step-like shape. I can divide it into three rectangles.
- Rectangle 1 (Bottom): Length = 6 units, Height = 3 units.
- Area = $6 \times 3 = 18$ square units.
- Rectangle 2 (Middle): Length = 6 units, Height = 6 units.
- Area = $6 \times 6 = 36$ square units.
- Rectangle 3 (Top): Length = 6 units, Height = 3 units.
- Area = $6 \times 3 = 18$ square units.
- Total Area: $18 + 36 + 18 = 72$ square units.
---
Problem 9 (Third Row, First from Left)
This is a combination of a triangle and a rectangle.
- Rectangle: Length = 8 units, Height = 10 units.
- Area = $8 \times 10 = 80$ square units.
- Triangle: Base = 18 units, Height = 4 units.
- Area = $\frac{1}{2} \times 18 \times 4 = 36$ square units.
- Total Area: $80 + 36 = 116$ square units.
---
Problem 10 (Third Row, Second from Left)
This is an arrow shape. I can divide it into a triangle and a rectangle.
- Rectangle: Length = 6 units, Height = 4 units.
- Area = $6 \times 4 = 24$ square units.
- Triangle: Base = 6 units, Height = 10 units.
- Area = $\frac{1}{2} \times 6 \times 10 = 30$ square units.
- Total Area: $24 + 30 = 54$ square units.
---
Problem 11 (Third Row, Third from Left)
This is a complex L-shape. I can divide it into two rectangles.
- Rectangle 1 (Left): Length = 16 units, Height = 22 units.
- Area = $16 \times 22 = 352$ square units.
- Rectangle 2 (Right): Length = 8 units, Height = 15 units.
- Area = $8 \times 15 = 120$ square units.
- Total Area: $352 + 120 = 472$ square units.
---
Problem 12 (Third Row, Fourth from Left)
This is an L-shape. I can divide it into two rectangles.
- Rectangle 1 (Vertical): Length = 16 units, Height = 16 units.
- Area = $16 \times 16 = 256$ square units.
- Rectangle 2 (Horizontal): Length = 12 units, Height = 3 units.
- Area = $12 \times 3 = 36$ square units.
- Total Area: $256 + 36 = 292$ square units.
---
Problem 13 (Fourth Row, First from Left)
This is an L-shape. I can divide it into two rectangles.
- Rectangle 1 (Vertical): Length = 8 units, Height = 30 units.
- Area = $8 \times 30 = 240$ square units.
- Rectangle 2 (Horizontal): Length = 34 units, Height = 15 units.
- Area = $34 \times 15 = 510$ square units.
- Total Area: $240 + 510 = 750$ square units.
---
Problem 14 (Fourth Row, Second from Left)
This shape is a rectangle with a semicircle on the left.
- Rectangle: Length = 22 units, Height = 10 units.
- Area = $22 \times 10 = 220$ square units.
- Semicircle: The diameter is 10 units, so the radius is 5 units.
- Area of a full circle = $\pi r^2 = \pi \times 5^2 = 25\pi$.
- Area of semicircle = $\frac{1}{2} \times 25\pi = 12.5\pi$ square units.
- Total Area: $220 + 12.5\pi$ square units.
---
Problem 15 (Fourth Row, Third from Left)
This is a complex shape. I can divide it into two rectangles.
- Rectangle 1 (Bottom): Length = 20 units, Height = 15 units.
- Area = $20 \times 15 = 300$ square units.
- Rectangle 2 (Top): Length = 16 units, Height = 5 units.
- Area = $16 \times 5 = 80$ square units.
- Total Area: $300 + 80 = 380$ square units.
---
Problem 16 (Fourth Row, Fourth from Left)
This is an L-shape. I can divide it into two rectangles.
- Rectangle 1 (Vertical): Length = 9 units, Height = 12 units.
- Area = $9 \times 12 = 108$ square units.
- Rectangle 2 (Horizontal): Length = 18 units, Height = 7 units.
- Area = $18 \times 7 = 126$ square units.
- Total Area: $108 + 126 = 234$ square units.
---
Problem 17 (Fifth Row, First from Left)
This is a complex shape. I can divide it into three rectangles.
- Rectangle 1 (Top): Length = 32 units, Height = 14 units.
- Area = $32 \times 14 = 448$ square units.
- Rectangle 2 (Left): Length = 11 units, Height = 9 units.
- Area = $11 \times 9 = 99$ square units.
- Rectangle 3 (Right): Length = 16 units, Height = 9 units.
- Area = $16 \times 9 = 144$ square units.
- Total Area: $448 + 99 + 144 = 691$ square units.
---
Problem 18 (Fifth Row, Second from Left)
This is a complex shape. I can divide it into three rectangles.
- Rectangle 1 (Top): Length = 16 units, Height = 18 units.
- Area = $16 \times 18 = 288$ square units.
- Rectangle 2 (Middle): Length = 34 units, Height = 18 units.
- Area = $34 \times 18 = 612$ square units.
- Rectangle 3 (Bottom): Length = 16 units, Height = 18 units.
- Area = $16 \times 18 = 288$ square units.
- Total Area: $288 + 612 + 288 = 1188$ square units.
---
Problem 19 (Fifth Row, Third from Left)
This is a rectangle with a smaller rectangle cut out from the top.
- Large Rectangle: Length = 30 units, Height = 20 units.
- Area = $30 \times 20 = 600$ square units.
- Cut-out Rectangle: Length = 18 units, Height = 6 units.
- Area = $18 \times 6 = 108$ square units.
- Total Area: $600 - 108 = 492$ square units.
---
Problem 20 (Fifth Row, Fourth from Left)
This is a combination of a triangle and a rectangle.
- Rectangle: Length = 10 units, Height = 28 units.
- Area = $10 \times 28 = 280$ square units.
- Triangle: Base = 24 units, Height = 12 units.
- Area = $\frac{1}{2} \times 24 \times 12 = 144$ square units.
- Total Area: $280 + 144 = 424$ square units.
---
Final Answer
Here are the areas for all 20 composite figures:
1. 44 square units
2. 33 square units
3. 72 square units
4. $32 + 2\pi$ square units
5. 76 square units
6. 136 square units
7. 190 square units
8. 72 square units
9. 116 square units
10. 54 square units
11. 472 square units
12. 292 square units
13. 750 square units
14. $220 + 12.5\pi$ square units
15. 380 square units
16. 234 square units
17. 691 square units
18. 1188 square units
19. 492 square units
20. 424 square units
Parent Tip: Review the logic above to help your child master the concept of composite figures worksheet 7th grade.
