Question

Find the area of the figure. 15 am 8 am

Answer 1

The figure shows a triangle and a semi-circle.

To find the area of the figure, we find the area of the triangle and add it to the area of the semi circle.

First, let's see the formula for the area of a triangle and the area of a semi circle.

Area of a Triangle

`A=(1)/(2)bh`

Where

b is the base length

h is the height of the triangle

Given,

h = 15

b = 16 [base length of triangle is the diameter, which is TWICE the radius (given as 8)]

Substituting, we find the area of the triangle. Shown below:

`\begin{gathered} A=(1)/(2)bh \\ A=(1)/(2)(16)(15) \\ A=120 \end{gathered}`

Now,

Area of Semi-Circle

The formula is:

`A=(\pi r^2)/(2)`

Where r is the radius

Given the radius is 8, we susbtitute it into the formula and find the area of the semicircle. Shown below:

`\begin{gathered} A=(\pi r^2)/(2) \\ A=(\pi(8)^2)/(2) \\ A=(64\pi)/(2) \\ A=32\pi \end{gathered}`

Thus,

Total Area of the Figure is

120 + 32π square cm

The answer, rounded to 2 decimal places, is:

220.53