Question

5. Michael wants to place grass on the sides of his

lap pool. Find the area of the shaded regions that
he wants to cover with grass.
25 yd
12 yd
3 yd
12 yd

Answer 1

204 square yards

Explanation:

We need to find the area of the whole trapezoid and then subtract the area of the rectangle from that.

The area of a trapezoid is denoted by:
`A=((b_1+b_2)*h)/(2)`, where b1 and b2 are the bases and h is the height. Here, the bases are 25 and 12 + 3 = 15, while the height is 12. So plug these values in:

`A=((b_1+b_2)*h)/(2)`

`A=((25+15)*12)/(2)=240` square yards

The area of a rectangle is A = lw, where l is the length and w is the width. Here the length is 12 and the width is 3, so the area is 12 * 3 = 36 square yards. Subtract this from the total 240:

240 - 36 = 204

The area of the shaded region is 204 yd squared.

Answer 2

Area of the shaded region to be covered with grass is 204 yd²

Explanation:

• Step 1: Area of the shaded region can be found by finding the total area and subtracting the area of the lap pool.

Total area = Area of the trapezium = 1/2 × (Sum of parallel sides) × distance between them

Sum of parallel sides = 25 yd + (3 + 12) = 40 yd

Distance between them = 12 yd

⇒ Total area = 1/2 × 40 × 12 = 240 yd²

• Step 2: Find the area of the lap pool.

Area = length × width = 12 × 3 = 36 yd²

• Step 3: Find the area of the shaded region

Area to be covered with grass = 240 - 36 = 204 yd²