Answer:
A = 8[tex]\pi[/tex] in.² + 12 in.²
A = (8[tex]\pi[/tex] + 12) in.²
Explanation:
To find the area of this object, divide it into recognizable shapes.
The first/top part could be divided into a semicircle, the second/bottom into a triangle.
Calculate the area of each of these separately and then add the two results together to find the overall area.
Area of the semicircle:
Use the area of the circle formula, which is: A = [tex]\pi[/tex]r²
However, since this formula will account for the area of a full circle, you will need to divide your answer by 2 at the end, hence finding the area of one half of a circle, a.k.a. a semicircle.
A = [tex]\pi[/tex](4)² Sub in value
A = 16[tex]\pi[/tex]
A = 8[tex]\pi[/tex] in.² Divide 16 by 2 to find area of semicircle of same radius
Area of the triangle:
Use the area of the triangle formula, which is: A = [tex]\frac{1}{2}[/tex]bh
You can work on finding the area of one triangle first, the one on the right.
You already have the values for b (base) and h (perpendicular height).
These can be found by visually flipping the triangle upside down.
Now, the value for b is 4 inches, and the value for h is 3. Use these in your formula.
A = [tex]\frac{1}{2}[/tex](4)(3) Sub in values
A = 6 in.²
You have found the area of the triangle on the right, however - there is still a triangle on the left. Therefore, multiply your answer by 2 and find the combined area of these two triangles.
A = 12 in.²
Area of the composite figure:
A = 8[tex]\pi[/tex] in.² + 12 in.²
A = (8[tex]\pi[/tex] + 12) in.²
