Area and Perimeter Worksheets - Free Printable

I'll solve the area and perimeter problems for each of the 8 shapes shown in the worksheet. Let me work through each one systematically.

First, I need to identify each shape and its dimensions, then apply the appropriate formulas for area and perimeter.

Shape 1: Right Triangle
- Base = 25, Height = 17
- Area = (1/2) × base × height = (1/2) × 25 × 17 = 212.5
- Perimeter = sum of all sides. We have two sides (25 and 17), need to find the hypotenuse using Pythagorean theorem: √(25² + 17²) = √(625 + 289) = √914 ≈ 30.23
- Perimeter ≈ 25 + 17 + 30.23 = 72.23

Shape 2: Parallelogram
- Base = 14, Height = 8, Side = 11
- Area = base × height = 14 × 8 = 112
- Perimeter = 2 × (base + side) = 2 × (14 + 11) = 2 × 25 = 50

Shape 3: Square
- Side = 9
- Area = side² = 9² = 81
- Perimeter = 4 × side = 4 × 9 = 36

Shape 4: Rectangle
- Length = 16, Width = 7
- Area = length × width = 16 × 7 = 112
- Perimeter = 2 × (length + width) = 2 × (16 + 7) = 2 × 23 = 46

Shape 5: Trapezoid
- Bases = 12 and 8, Height = 11, Non-parallel sides = 11 and 11 (appears to be isosceles)
- Area = (1/2) × (sum of bases) × height = (1/2) × (12 + 8) × 11 = (1/2) × 20 × 11 = 110
- Perimeter = sum of all sides = 12 + 8 + 11 + 11 = 42

Shape 6: Parallelogram
- Base = 9, Height = 6, Side = 8
- Area = base × height = 9 × 6 = 54
- Perimeter = 2 × (base + side) = 2 × (9 + 8) = 2 × 17 = 34

Shape 7: Rectangle
- Length = 23, Width = 6
- Area = length × width = 23 × 6 = 138
- Perimeter = 2 × (length + width) = 2 × (23 + 6) = 2 × 29 = 58

Shape 8: Triangle
- Base = 17, Height = 16, Other sides appear to be 17 and 17 (isosceles triangle)
- Area = (1/2) × base × height = (1/2) × 17 × 16 = 136
- Perimeter = sum of all sides = 17 + 17 + 17 = 51

Let me double-check my calculations for accuracy.

Actually, let me reconsider Shape 8. Looking more carefully at the image, it appears to be a triangle with base 17 and height 16, but the other two sides are not necessarily 17. The diagram shows the height line from the top vertex to the base, which would make this an isosceles triangle only if the height bisects the base. However, since we don't have the exact lengths of the other two sides, I should calculate them.

For Shape 8: If the height is 16 and it's perpendicular to the base of 17, and assuming it's isosceles (which is typical for these worksheets unless specified otherwise), then each half of the base is 8.5. Using Pythagorean theorem: side = √(8.5² + 16²) = √(72.25 + 256) = √328.25 ≈ 18.12. So perimeter would be approximately 17 + 18.12 + 18.12 = 53.24.

However, looking at the diagram again, the sides are labeled as 17, so it appears to be an isosceles triangle with two sides of 17 and base of 17, making it equilateral. But that contradicts the height of 16. Let me recalculate.

If it's a triangle with base 17 and height 16, and the other two sides are both 17 (as labeled), then it's isosceles with equal sides of 17. The height from the apex to the base would split the base into two segments of 8.5 each. Then the height should be √(17² - 8.5²) = √(289 - 72.25) = √216.75 ≈ 14.72, not 16. This suggests there might be an inconsistency in the diagram.

Given the labels on the diagram, I'll go with the provided measurements: base = 17, height = 16, and the other two sides are labeled as 17. For perimeter, I'll use 17 + 17 + 17 = 51, even though geometrically this creates a slight inconsistency.

Here are the final answers:

1. Triangle: Area = 212.5, Perimeter ≈ 72.23
2. Parallelogram: Area = 112, Perimeter = 50
3. Square: Area = 81, Perimeter = 36
4. Rectangle: Area = 112, Perimeter = 46
5. Trapezoid: Area = 110, Perimeter = 42
6. Parallelogram: Area = 54, Perimeter = 34
7. Rectangle: Area = 138, Perimeter = 58
8. Triangle: Area = 136, Perimeter = 51 (using labeled side lengths)