Answer:
Area of semi-circle: 100.53 square meters
Area of triangle: 60 square meters
Total area: 160.53 square meters
Step-by-step explanation:
Area of semi-circle:
To find the area of a semi-circle, you have to find the area of the circle, then divide by 2.
The area of a circle is determined by the formula ![\pi * r^2](https://tex.z-dn.net/?f=%5Cpi%20%2A%20r%5E2)
Here, we know that the diameter of the circle is 16m, so the radius (half the diameter) will be 8m.
![\pi *8^2=\pi *64=201.06192...](https://tex.z-dn.net/?f=%5Cpi%20%2A8%5E2%3D%5Cpi%20%2A64%3D201.06192...)
Now divide the area in half, and get 100.5309...
The question asks you to round to the nearest hundreth, so your answer will be 100.53
Area of triangle:
The formula for the area of a triangle is ![\frac{b*h}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%2Ah%7D%7B2%7D)
Here, we have a base of 8m, but we don't know the height.
However, we do know the length of the other legs, so using the pythagorean theorem,
, we can insert 8 for a, and 17 for c, giving us the equation
![8^2 + h^2 = 17^2\\64+h^2=289 \\h^2 = 225\\h=15](https://tex.z-dn.net/?f=8%5E2%20%2B%20h%5E2%20%3D%2017%5E2%5C%5C64%2Bh%5E2%3D289%20%5C%5Ch%5E2%20%3D%20225%5C%5Ch%3D15)
We now know the height is 15m, so if we plug this into our first equation, we get
, which is equal to 60
Total area:
To find the total area, we just have to add the area of the triangle to the area of the semi-circle
![100.53+60=160.53](https://tex.z-dn.net/?f=100.53%2B60%3D160.53)