Question

What is the perimeter of the following composite figure?

12 yd
9 yd
O 35.13 yd
O 21 yd
O 47.13 yd
O 42 yd

Answer 1

139.79 yd^2

108 + 31.79 = 139.79

Step-by-step explanation:

Rectangle's Area

12 x 9 = 108

Semi Circle's Area

9 x 9 = 81

81 x 3.14 = 254.34

254.34/8 = 31.79

The semi circle's 2 formulas are πr^2/2 and πd^2/8.

Use πd^2/8 if you are using the diameter

the d stands for diameter

Use πr^2/2 if you are using the radius

the r stands for radius

This is what I used for the semi circle

3.14 x 9^2/8

You can also use this

3.14 x 4.5^2/2

Both of those work and you will get the same results.

Answer 2

C

Step-by-step explanation:

Here, we have a rectangle and a semi-circle and we want to calculate the area of the given shape

To get this, we add the area of the rectangle to the area of the semi-circle

The area of the rectangle is 12 * 9 = 108 square yard

From the diagram, we can see that 9 yards represent the diameter of the semi-circle

What we need to get the area of the semi-circle is the radius and this is half of the diameter

In this case, the half of the diameter is 9/2 = 4.5 yards

The area would be pi * r^2/2

= 3.142 * 4.5^2 = 63.6255/2 = 31.81275 square yards

We proceed to add this to the area of the rectangle

Mathematically, that would be ;

31.81275 + 108 = 139.81275 square yards

The closest answer here is 139.79 which we are going to select

The reason for the answer difference is the version of pi used

Pi could be 22/7 or 3.142

Using both will lead to different answers before approximation