Question

1. Find the area of the composite figure to the nearest hundredth.

2. Find the area of the shaded region to the nearest tenth.

Answer 1

#1: 751.56 mm²

#2: 477 km²

Explanation:

First I noted the semicircle on the left, which has a radius of 12.5 mm. The formula for finding the area of a semicircle is 1/2(πr²).

1/2(3.14 * (12.5)²)

12.5 squared is 156.25.

1/2(3.14 * 156.25)

Multiply 3.14 by 156.25 to get 490.625.

1/2(490.625)

Divide 490.625 by 2 to get 245.3125.

245.3125 mm² for the semicircle

Then, I split the rest of into a 12.5 by 25 rectangle and a 31 by 12.5 triangle.

(12.5 * 25) + 1/2(31 * 12.5)

Multiply 12.5 by 25 to get 312.5.

312.5 + 1/2(31 * 12.5)

Multiply 31 by 12.5 to get 387.5.

312.5 + 1/2(387.5)

Multiply 1/2 by 387.5 to get 193.75

312.5 + 193.75

Add 312.5 and 193.75 to get 506.25.

506.25 mm² for the rest of the figure.

Now add the two measures, and you have your answer for #1.

245.3125 + 506.25 = 751.5625 mm², which rounds to 751.56 mm².

The area of the composite figure is 751.56 mm².

Now for #2. First, find the area of the triangle.

1/2(40 * 27)

Multiply 40 by 27 to get 1080.

1/2(1080)

Multiply 1/2 by 1080.

590 km² for the triangle.

Now find the area of the circle.

3.14 * 6²

3.14 * 36

113.04 km² for the circle.

Now subtract the area of the circle from the area of the triangle.

590 - 113.04

476.96 km², which rounds to 477.0 km².

The area of the shaded region is 477 km².

Answer 2

• 1. 745.31 mm²
• 2. 426.96 km²

Explanation:

#1

We can separate the figure into 3 parts and sum the areas.

Semicircle with radius 12.5 mm:

• A = 1/2(πr²) = 1/2(3.14*12.5²) = 245.31 mm²

Rectangle with sides 12.5 mm and its double size:

• A = 12.5*(2*12.5) = 312.5 mm²

Triangle with height 12.5 mm and base 30 mm:

• A = 1/2*(55 - 2*12.5)*12.5 = 187.5 mm²

Sum of the three:

• 245.31 + 312.5 + 187.5 = 745.31 mm²

#2

The shaded region is the difference of the areas of the triangle and the circle

Triangle:

• A = 1/2*27*40 = 540 km²

Circle:

• A = πr² = πd²/4 = 3.14*12²/4 = 113.04 km²

Shaded region:

• 540 - 113.04 = 426.96 km²