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3 years ago

If anyone could please help me with this I would greatly appreciate it!!

Mathematics

1 answer:

Dimas [21]3 years ago

7 0

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

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<u>Solution: </u>

Given that

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Cost of full price of year book = $\$45$ each

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Total price spent by 24 students to purchase year book = $\$975$

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