Find the area of composite shapes with this math worksheet.
Worksheet titled "Area" with three composite shapes to find the area, including a diamond with a rectangle, an L-shaped figure, and a U-shaped figure, each with labeled dimensions.
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Show Answer Key & Explanations
Step-by-step solution for: Composing Shapes | Definition, Examples, Perimeter, How To Measure
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Show Answer Key & Explanations
Step-by-step solution for: Composing Shapes | Definition, Examples, Perimeter, How To Measure
Let’s solve each problem step by step.
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Problem 1:
We have a composite shape made of a rectangle in the middle and two triangles on the sides.
- The rectangle is 12m tall and 3m wide → Area = 12 × 3 = 36 m²
- Each triangle has:
- Base = 6cm? Wait — that can’t be right. Look again.
Actually, looking at the diagram:
The dashed line goes across the whole width. The total width from left to right tip is not given directly, but we see:
- The rectangle is 3m wide.
- On each side, there’s a triangle with base extending from the rectangle edge to the tip.
- The label “6cm” is probably a typo — it should be 6m, because everything else is in meters (12m, 3m). Also, area would be tiny if it were cm. So we’ll assume 6m.
Each triangle has:
- Height = half of 12m? No — wait, the height of each triangle is actually the full 12m? Let’s think.
Actually, the dashed line is horizontal through the center. That means each triangle is split into two right triangles? Or maybe the whole triangle on one side has base 6m and height 6m?
Wait — better approach:
Looking at the shape: It looks like a diamond (rhombus) with a rectangle inside? Actually, no — it's a central rectangle with two triangles attached on left and right.
But the dashed line suggests symmetry. The total height is 12m. The rectangle is 3m wide. The triangles extend out 6m on each side? But then the base of each triangle would be 12m (height of rectangle), and the "width" of the triangle (from rectangle edge to tip) is 6m.
Actually, for a triangle, area = ½ × base × height.
If we consider each side triangle:
- The base of the triangle is the same as the height of the rectangle → 12m
- The height of the triangle (perpendicular distance from base to tip) is 6m
So area of one triangle = ½ × 12 × 6 = 36 m²
There are two such triangles → 36 × 2 = 72 m²
Plus the rectangle: 12 × 3 = 36 m²
Total area = 72 + 36 = 108 m²
Wait — let me double-check.
Alternative view: The entire shape is a rhombus? Or a kite?
Actually, if you look at the outer points: top, bottom, left, right.
From left tip to right tip: 6m (left triangle) + 3m (rectangle) + 6m (right triangle) = 15m total width.
Height is 12m.
But it’s not a rectangle — it’s pointed on left and right.
Actually, this shape is made of two identical trapezoids? Or perhaps easier: it’s a rectangle plus two triangles.
Yes — and each triangle has base = 12m (vertical side) and height = 6m (horizontal extension).
Area of triangle = ½ × base × height = ½ × 12 × 6 = 36 m² per triangle.
Two triangles: 72 m²
Rectangle: 12 × 3 = 36 m²
Total: 72 + 36 = 108 m²
✔ Confirmed.
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Problem 2:
This is an L-shaped figure.
We can break it into two rectangles.
Option 1: Split vertically.
Left part: width = 9cm - 3cm = 6cm, height = 8cm → area = 6 × 8 = 48 cm²
Right part: width = 3cm, height = 3cm → area = 3 × 3 = 9 cm²
Total = 48 + 9 = 57 cm²
Option 2: Split horizontally.
Bottom part: width = 9cm, height = 3cm → area = 9 × 3 = 27 cm²
Top part: width = 6cm (since 9 - 3 = 6), height = 5cm (8 - 3 = 5) → area = 6 × 5 = 30 cm²
Total = 27 + 30 = 57 cm²
Same answer.
✔ Confirmed.
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Problem 3:
Another composite shape — looks like a big rectangle with a smaller rectangle cut out from the middle-right.
Outer dimensions: 12m wide, 10m high.
But there’s a notch: from the right side, going in 8m, and down 6m, leaving 2m at top and 2m at bottom.
So, we can calculate area as:
Big rectangle minus the missing piece.
Big rectangle: 12 × 10 = 120 m²
Missing piece: it’s a rectangle that is 8m wide and 6m high? Let’s see.
From the diagram:
- Total height = 10m
- Top strip = 2m
- Bottom strip = 2m
- So middle section height = 10 - 2 - 2 = 6m → matches the labeled 6m
Width of missing part: labeled 8m
So missing rectangle: 8m × 6m = 48 m²
Therefore, area of shape = 120 - 48 = 72 m²
Alternatively, add up the parts:
Left vertical strip: width = 12 - 8 = 4m, height = 10m → area = 4 × 10 = 40 m²
Top horizontal strip (on the right): width = 8m, height = 2m → area = 8 × 2 = 16 m²
Bottom horizontal strip (on the right): width = 8m, height = 2m → area = 8 × 2 = 16 m²
Total = 40 + 16 + 16 = 72 m²
✔ Confirmed.
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Final Answer:
1. 108
2. 57
3. 72
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Problem 1:
We have a composite shape made of a rectangle in the middle and two triangles on the sides.
- The rectangle is 12m tall and 3m wide → Area = 12 × 3 = 36 m²
- Each triangle has:
- Base = 6cm? Wait — that can’t be right. Look again.
Actually, looking at the diagram:
The dashed line goes across the whole width. The total width from left to right tip is not given directly, but we see:
- The rectangle is 3m wide.
- On each side, there’s a triangle with base extending from the rectangle edge to the tip.
- The label “6cm” is probably a typo — it should be 6m, because everything else is in meters (12m, 3m). Also, area would be tiny if it were cm. So we’ll assume 6m.
Each triangle has:
- Height = half of 12m? No — wait, the height of each triangle is actually the full 12m? Let’s think.
Actually, the dashed line is horizontal through the center. That means each triangle is split into two right triangles? Or maybe the whole triangle on one side has base 6m and height 6m?
Wait — better approach:
Looking at the shape: It looks like a diamond (rhombus) with a rectangle inside? Actually, no — it's a central rectangle with two triangles attached on left and right.
But the dashed line suggests symmetry. The total height is 12m. The rectangle is 3m wide. The triangles extend out 6m on each side? But then the base of each triangle would be 12m (height of rectangle), and the "width" of the triangle (from rectangle edge to tip) is 6m.
Actually, for a triangle, area = ½ × base × height.
If we consider each side triangle:
- The base of the triangle is the same as the height of the rectangle → 12m
- The height of the triangle (perpendicular distance from base to tip) is 6m
So area of one triangle = ½ × 12 × 6 = 36 m²
There are two such triangles → 36 × 2 = 72 m²
Plus the rectangle: 12 × 3 = 36 m²
Total area = 72 + 36 = 108 m²
Wait — let me double-check.
Alternative view: The entire shape is a rhombus? Or a kite?
Actually, if you look at the outer points: top, bottom, left, right.
From left tip to right tip: 6m (left triangle) + 3m (rectangle) + 6m (right triangle) = 15m total width.
Height is 12m.
But it’s not a rectangle — it’s pointed on left and right.
Actually, this shape is made of two identical trapezoids? Or perhaps easier: it’s a rectangle plus two triangles.
Yes — and each triangle has base = 12m (vertical side) and height = 6m (horizontal extension).
Area of triangle = ½ × base × height = ½ × 12 × 6 = 36 m² per triangle.
Two triangles: 72 m²
Rectangle: 12 × 3 = 36 m²
Total: 72 + 36 = 108 m²
✔ Confirmed.
---
Problem 2:
This is an L-shaped figure.
We can break it into two rectangles.
Option 1: Split vertically.
Left part: width = 9cm - 3cm = 6cm, height = 8cm → area = 6 × 8 = 48 cm²
Right part: width = 3cm, height = 3cm → area = 3 × 3 = 9 cm²
Total = 48 + 9 = 57 cm²
Option 2: Split horizontally.
Bottom part: width = 9cm, height = 3cm → area = 9 × 3 = 27 cm²
Top part: width = 6cm (since 9 - 3 = 6), height = 5cm (8 - 3 = 5) → area = 6 × 5 = 30 cm²
Total = 27 + 30 = 57 cm²
Same answer.
✔ Confirmed.
---
Problem 3:
Another composite shape — looks like a big rectangle with a smaller rectangle cut out from the middle-right.
Outer dimensions: 12m wide, 10m high.
But there’s a notch: from the right side, going in 8m, and down 6m, leaving 2m at top and 2m at bottom.
So, we can calculate area as:
Big rectangle minus the missing piece.
Big rectangle: 12 × 10 = 120 m²
Missing piece: it’s a rectangle that is 8m wide and 6m high? Let’s see.
From the diagram:
- Total height = 10m
- Top strip = 2m
- Bottom strip = 2m
- So middle section height = 10 - 2 - 2 = 6m → matches the labeled 6m
Width of missing part: labeled 8m
So missing rectangle: 8m × 6m = 48 m²
Therefore, area of shape = 120 - 48 = 72 m²
Alternatively, add up the parts:
Left vertical strip: width = 12 - 8 = 4m, height = 10m → area = 4 × 10 = 40 m²
Top horizontal strip (on the right): width = 8m, height = 2m → area = 8 × 2 = 16 m²
Bottom horizontal strip (on the right): width = 8m, height = 2m → area = 8 × 2 = 16 m²
Total = 40 + 16 + 16 = 72 m²
✔ Confirmed.
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Final Answer:
1. 108
2. 57
3. 72
Parent Tip: Review the logic above to help your child master the concept of area of composite figures worksheets.
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