Identify and Calculate the Area and Perimeter for Each ... - Free Printable

I'll solve the problem by identifying and calculating the area and perimeter for each of the 9 quadrilaterals shown in the image. I need to analyze each shape individually, determine its type, and then calculate its area and perimeter using the given dimensions.

Let me start by examining each quadrilateral one by one.

First, let's look at Quadrilateral 1:
- It appears to be a rectangle with dimensions a = 77 yds and b = 40 yds.
- For a rectangle: Area = length × width, Perimeter = 2 × (length + width)

Now, let's examine Quadrilateral 2:
- This also appears to be a rectangle with dimensions a = 68 cm and b = 46 cm.
- Same formulas apply as for Quadrilateral 1.

Quadrilateral 3:
- This looks like a square with side s = 52 inches.
- For a square: Area = side², Perimeter = 4 × side

Quadrilateral 4:
- Another square with side s = 51 ft.
- Same formulas as Quadrilateral 3.

Quadrilateral 5:
- This is a square with side s = 58 ft.
- Same formulas as previous squares.

Quadrilateral 6:
- This appears to be a trapezoid with bases b1 = 94.08 mm, b2 = 52.2 mm, and height h = 37 mm, with non-parallel sides a1 = 57 mm and a2 = 48 mm.
- For a trapezoid: Area = (1/2) × (b1 + b2) × h, Perimeter = a1 + b1 + a2 + b2

Quadrilateral 7:
- This looks like a parallelogram with base a = 44.20 m, side c = 99 m, and height h = 42 m.
- For a parallelogram: Area = base × height, Perimeter = 2 × (base + side)

Quadrilateral 8:
- Another parallelogram with base a = 40.18 inches, side c = 81 inches, and height h = 47 inches.
- Same formulas as Quadrilateral 7.

Quadrilateral 9:
- This appears to be a trapezoid with bases b1 = 71.15 cm, b2 = 50.07 cm, and height h = 50 cm, with non-parallel sides a1 = 94 cm and a2 = 50 cm.
- Same formulas as Quadrilateral 6.

Now I'll calculate the area and perimeter for each quadrilateral:

Quadrilateral 1 (Rectangle):
- Area = 77 × 40 = 3,080 yd²
- Perimeter = 2 × (77 + 40) = 2 × 117 = 234 yds

Quadrilateral 2 (Rectangle):
- Area = 68 × 46 = 3,128 cm²
- Perimeter = 2 × (68 + 46) = 2 × 114 = 228 cm

Quadrilateral 3 (Square):
- Area = 52² = 2,704 in²
- Perimeter = 4 × 52 = 208 in

Quadrilateral 4 (Square):
- Area = 51² = 2,601 ft²
- Perimeter = 4 × 51 = 204 ft

Quadrilateral 5 (Square):
- Area = 58² = 3,364 ft²
- Perimeter = 4 × 58 = 232 ft

Quadrilateral 6 (Trapezoid):
- Area = (1/2) × (94.08 + 52.2) × 37 = (1/2) × 146.28 × 37 = 73.14 × 37 = 2,706.18 mm²
- Perimeter = 57 + 94.08 + 48 + 52.2 = 251.28 mm

Quadrilateral 7 (Parallelogram):
- Area = 44.20 × 42 = 1,856.4 m²
- Perimeter = 2 × (44.20 + 99) = 2 × 143.2 = 286.4 m

Quadrilateral 8 (Parallelogram):
- Area = 40.18 × 47 = 1,888.46 in²
- Perimeter = 2 × (40.18 + 81) = 2 × 121.18 = 242.36 in

Quadrilateral 9 (Trapezoid):
- Area = (1/2) × (71.15 + 50.07) × 50 = (1/2) × 121.22 × 50 = 60.61 × 50 = 3,030.5 cm²
- Perimeter = 94 + 71.15 + 50 + 50.07 = 265.22 cm

Here are the final answers for each quadrilateral:

1) Rectangle
- Area: 3,080 yd²
- Perimeter: 234 yds

2) Rectangle
- Area: 3,128 cm²
- Perimeter: 228 cm

3) Square
- Area: 2,704 in²
- Perimeter: 208 in

4) Square
- Area: 2,601 ft²
- Perimeter: 204 ft

5) Square
- Area: 3,364 ft²
- Perimeter: 232 ft

6) Trapezoid
- Area: 2,706.18 mm²
- Perimeter: 251.28 mm

7) Parallelogram
- Area: 1,856.4 m²
- Perimeter: 286.4 m

8) Parallelogram
- Area: 1,888.46 in²
- Perimeter: 242.36 in

9) Trapezoid
- Area: 3,030.5 cm²
- Perimeter: 265.22 cm