Math worksheet to calculate area and perimeter of different polygons.

Let's solve each polygon one by one, calculating the Area, Perimeter, and identifying the Type of polygon.

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1) Rectangle

- $ a = 88 \text{ cm},\ b = 59 \text{ cm} $
- Type: Rectangle (Opposite sides equal, all angles 90°)

Area = $ a \times b = 88 \times 59 = 5192 \text{ cm}^2 $

Perimeter = $ 2(a + b) = 2(88 + 59) = 2(147) = 294 \text{ cm} $

✔ Answer:
- Area: 5192 cm²
- Perimeter: 294 cm
- Type: Rectangle

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2) Rectangle

- $ a = 72 \text{ inches},\ b = 46 \text{ inches} $
- Type: Rectangle

Area = $ 72 \times 46 = 3312 \text{ in}^2 $

Perimeter = $ 2(72 + 46) = 2(118) = 236 \text{ inches} $

✔ Answer:
- Area: 3312 in²
- Perimeter: 236 inches
- Type: Rectangle

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3) Triangle (Isosceles)

- $ a = 40 \text{ ft},\ b = 72 \text{ ft} $ (two equal sides)
- Type: Isosceles Triangle (Two sides equal)

We need to find area. But we don’t have height. We can use Heron’s formula.

Sides: $ a = 40,\ b = 72,\ c = 72 $

Semi-perimeter $ s = \frac{40 + 72 + 72}{2} = \frac{184}{2} = 92 $

Area = $ \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{92(92-40)(92-72)(92-72)} $

= $ \sqrt{92 \times 52 \times 20 \times 20} $

= $ \sqrt{92 \times 52 \times 400} $

First compute:
- $ 92 \times 52 = 4784 $
- $ 4784 \times 400 = 1,913,600 $

So,
- $ \sqrt{1,913,600} \approx 1383.3 \text{ ft}^2 $

Alternatively, use triangle area with base and height:

But we don’t have height. So Heron’s is best.

✔ Answer:
- Area: ≈ 1383.3 ft²
- Perimeter: $ 40 + 72 + 72 = 184 \text{ ft} $
- Type: Isosceles Triangle

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4) Triangle (Isosceles)

- $ a = 38 \text{ yds},\ b = 75 \text{ yds} $ → two equal sides
- So sides: 75, 75, 38
- Type: Isosceles Triangle

Use Heron’s formula again.

$ s = \frac{75 + 75 + 38}{2} = \frac{188}{2} = 94 $

Area = $ \sqrt{94(94 - 75)(94 - 75)(94 - 38)} $

= $ \sqrt{94 \times 19 \times 19 \times 56} $

Compute step-by-step:
- $ 94 \times 56 = 5264 $
- $ 19 \times 19 = 361 $
- $ 5264 \times 361 = ? $

Better: $ \sqrt{94 \times 19^2 \times 56} = 19 \times \sqrt{94 \times 56} $

$ 94 \times 56 = 5264 $

$ \sqrt{5264} \approx 72.56 $

So $ 19 \times 72.56 \approx 1378.6 \text{ yd}^2 $

✔ Answer:
- Area: ≈ 1378.6 yd²
- Perimeter: $ 75 + 75 + 38 = 188 \text{ yds} $
- Type: Isosceles Triangle

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5) Square

- $ s = 63 \text{ mm} $
- Type: Square

Area = $ s^2 = 63^2 = 3969 \text{ mm}^2 $

Perimeter = $ 4s = 4 \times 63 = 252 \text{ mm} $

✔ Answer:
- Area: 3969 mm²
- Perimeter: 252 mm
- Type: Square

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6) Square

- $ s = 65 \text{ yds} $
- Type: Square

Area = $ 65^2 = 4225 \text{ yd}^2 $

Perimeter = $ 4 \times 65 = 260 \text{ yds} $

✔ Answer:
- Area: 4225 yd²
- Perimeter: 260 yds
- Type: Square

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7) Parallelogram

- $ a = 54.96 \text{ ft},\ c = 89 \text{ ft},\ h = 52 \text{ ft} $
- In a parallelogram, opposite sides are equal.
- So sides: $ a = 54.96,\ c = 89 $
- Type: Parallelogram

Area = base × height = $ c \times h = 89 \times 52 = 4628 \text{ ft}^2 $

Perimeter = $ 2(a + c) = 2(54.96 + 89) = 2(143.96) = 287.92 \text{ ft} $

✔ Answer:
- Area: 4628 ft²
- Perimeter: 287.92 ft
- Type: Parallelogram

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8) Trapezoid

- $ a1 = 100 \text{ cm},\ a2 = 43 \text{ cm} $
- $ b1 = 68.28 \text{ cm},\ b2 = 58.8 \text{ cm} $
- $ h = 56 \text{ cm} $
- Type: Trapezoid (one pair of parallel sides — assume $ a1 $ and $ a2 $ are the bases)

Wait: typically, $ a1 $ and $ a2 $ are the two bases (parallel sides), and $ b1, b2 $ are the non-parallel legs.

So:
- Bases: $ a1 = 100 \text{ cm},\ a2 = 43 \text{ cm} $
- Legs: $ b1 = 68.28 \text{ cm},\ b2 = 58.8 \text{ cm} $
- Height: $ h = 56 \text{ cm} $

Area = $ \frac{1}{2}(a1 + a2) \times h = \frac{1}{2}(100 + 43) \times 56 = \frac{1}{2}(143) \times 56 = 71.5 \times 56 $

Calculate:
- $ 70 \times 56 = 3920 $
- $ 1.5 \times 56 = 84 $
- Total = $ 3920 + 84 = 4004 \text{ cm}^2 $

Perimeter = sum of all sides:
= $ a1 + a2 + b1 + b2 = 100 + 43 + 68.28 + 58.8 = 270.08 \text{ cm} $

✔ Answer:
- Area: 4004 cm²
- Perimeter: 270.08 cm
- Type: Trapezoid

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9) Parallelogram

- $ a = 61 \text{ inches},\ h = 55.28 \text{ inches} $
- Since it's a parallelogram, opposite sides are equal.
- Base = $ a = 61 $, height = $ h = 55.28 $
- But we don’t have the other side length? Wait — only one side given?

Wait: in the diagram, it shows $ a $ on both bottom and top, and side labeled $ a $? That suggests all sides equal?

No — in a parallelogram, opposite sides equal. But here, only one side $ a $ is labeled, and height $ h $ is given.

So likely: base = $ a = 61 $, height = $ h = 55.28 $, but side length not given? Wait — the figure shows only one side labeled as 'a', but in parallelogram, there are two pairs.

But perhaps this is a rhombus or just a general parallelogram?

But no other side is given.

Wait — looking at the diagram: it shows $ a $ on the base and the left side also labeled $ a $? That would mean all sides are $ a $? Then it's a rhombus.

But in that case, side = 61 inches, and height = 55.28 inches.

So:
- Type: Rhombus (all sides equal)

Area = base × height = $ 61 \times 55.28 $

Calculate:
- $ 60 \times 55.28 = 3316.8 $
- $ 1 \times 55.28 = 55.28 $
- Total = $ 3372.08 \text{ in}^2 $

Perimeter = $ 4 \times a = 4 \times 61 = 244 \text{ inches} $

✔ Answer:
- Area: 3372.08 in²
- Perimeter: 244 inches
- Type: Rhombus

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## ✔ Final Answers Summary:

| # | Area | Perimeter | Type |
|---|------|-----------|------|
| 1 | 5192 cm² | 294 cm | Rectangle |
| 2 | 3312 in² | 236 in | Rectangle |
| 3 | ≈1383.3 ft² | 184 ft | Isosceles Triangle |
| 4 | ≈1378.6 yd² | 188 yd | Isosceles Triangle |
| 5 | 3969 mm² | 252 mm | Square |
| 6 | 4225 yd² | 260 yd | Square |
| 7 | 4628 ft² | 287.92 ft | Parallelogram |
| 8 | 4004 cm² | 270.08 cm | Trapezoid |
| 9 | 3372.08 in² | 244 in | Rhombus |

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