Answer:
The area of the house is approximately 309.54 feet²
Step-by-step explanation:
* Lets describe the figure
- It has a quarter circle with radius = the width of the rectangle
- It has a rectangle with length = 26 - the length of the radius, and
width 10 feet
- It has a triangle with base equal the length of the rectangle and
height 8 feet
- It has a trapezoid, the length of its two parallel bases are 2 , 5 and
height 2 feet
* Lets revise the area of all the shape above
- Area the quarter circle = 1/4 π r²
- Area of the rectangle = length × width
- Area of the triangle = 1/2 × base × height
- Area of the trapezoid = 1/2( the sum of the parallel bases) × height
* Now lets solve the problem
# Area of the quarter circle
∵ The radius of the circle = the width of the rectangle
∵ The width of the rectangle = 10 feet
∴ The radius of the circle = 10 feet
∵ The area of the quarter circle = 1/4 π r²
∴ Its area = 1/4 π (10)² = 25π feet²
# Area of the rectangle
∵ The length of the rectangle = 26 - the length of the radius
∵ the length of the radius = 10 feet
∴ The length of the rectangle = 26 - 10 = 16 feet
∵ The width of the rectangle = 10 feet
∵ The area of the rectangle = length × width
∴ Its area = 16 × 10 = 160 feet²
# Area of the triangle
∵ The base = the length of the rectangle
∵ The length of the rectangle = 16 feet
∴ The base = 16 feet
∵ The height = 8 feet
∵ The area of the triangle = 1/2 × base × height
∴ Its area = 1/2 × 16 × 8 = 64 feet²
# Area of the trapezoid
∵ The length of its two parallel bases are 2 feet , 5 feet
∵ The height = 2 feet
∵ The area = 1/2( the sum of the parallel bases) × height
∴ Its area = 1/2 (2 + 5) × 2 = 7 feet²
- Lets add all of these areas to find the area of the house
∴ The area of the house = 25π + 160 + 64 + 7 = 309.5398 feet²
* The area of the house is approximately 309.54 feet²
