Question

Find the area of the composite figure... please help

Answer 1

27.5 yards^2

Explanation:

We are given a figure which comprises of two shapes: a rectangle and a semicircle and we are to find the area of this composite figure.

We know that the area of these two shapes is given by the following formulas so we will put in the given values to get:

Area of rectangle =
`length * width` =
`6 * 4` = 24 yd^2

Area of semi-circle =
`(\pi r^2)/(2)` =
`(3.14 * 1.5^2)/(2)` = 3.53 yd^2

Area of composite figure =
`24+3.53` = 27.5 yards^2

Answer 2

27.5 square yards

Explanation:

So, we have two shapes connected together and we want to know the combined area of the two. All we have to do is find out the area of each one, then add the results.

First, the rectangle:

The area of a rectangle is the base multiplied by the height, so

A = 6 x 4 = 24 square yards

Then, the half-circle.

We know the area of a circle is calculated with A = π * r², so the area of a half circle will be A = (π * r²)/2.

We know the circle has a diameter of 3 yards because the wall next to it is also 3 yards and the whole structure is 6 yards wide, so...

A = (π (1.5)²)/2 = 2.25 π / 2 = 3.53 square yards

Overall, we have

Area of the rectangle: 24 square yards

Area of the half-circle: 3.53 square yards

Total: 27.53 square yards, rounded to the tenth: 27.5 square yards.