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 [tex]\pi * r^2[/tex]
Here, we know that the diameter of the circle is 16m, so the radius (half the diameter) will be 8m.
[tex]\pi *8^2=\pi *64=201.06192...[/tex]
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 [tex]\frac{b*h}{2}[/tex]
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, [tex]a^2 + b^2 = c^2[/tex], we can insert 8 for a, and 17 for c, giving us the equation
[tex]8^2 + h^2 = 17^2\\64+h^2=289 \\h^2 = 225\\h=15[/tex]
We now know the height is 15m, so if we plug this into our first equation, we get [tex]\frac{8*15}{2}[/tex], 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
[tex]100.53+60=160.53[/tex]
