Answer:
- area: 16.28 ft²
- perimeter: 17.05 ft
Step-by-step explanation:
The figure is shown as being composed of a semicircle and a triangle. You know the formula for the area of a circle is ...
A = πr²
The radius of the semicircle is half its diameter, so is (4 ft)/2 = 2 ft. Then the area of a circle with radius 2 feet is ...
A = π(2 ft)² = 4π ft²
Our semicircle has half that area, so ...
area of semicircle = (4π ft²)/2 = 2π ft² ≈ 6.283 ft²
__
The area of the triangle is given by the formula ...
A = (1/2)bh
Here, the base is shown as 4 ft, and the height is shown as 5 ft. Then the triangle area is ...
triangle area = (1/2)(4 ft)(5 ft) = 10 ft²
So, the total area of the composite figure is ...
figure area = area of semicircle + triangle area
= 6.283 ft² + 10 ft² ≈ 16.283 ft² . . . . area of the figure
__
The perimeter of the curved portion of the semicircle is half the circumference of a circle of radius 2 ft. It will be ...
curved perimeter = (1/2)(2πr) = πr = π(2 ft) = 2π ft ≈ 6.283 ft
The length of each side of the triangle can be found from the Pythagorean theorem. Each side of the triangle is the hypotenuse of a right triangle with legs 2 ft and 5 ft. Then it will be ...
triangle side length = √(2² +5²) ft = √29 ft ≈ 5.385 ft
The total perimeter is ...
perimeter = 2 × triangle side length + semicircle length
= 2×(5.385 ft) + 6.283 ft = 17.054 ft
The perimeter of the figure is about 17.05 feet.
