Question

The front of a house is composed of a trapezoid and a rectangle. The height of the rectangle is 12 feet. The base of therectangle and one base of the trapezoid each measure 30 feet. The height of the trapezoid is 15 feet and its second basemeasures 10 feet.What is the area of the front of the house in square feet?Draw and label a diagram to help you solve the problem

Answer 1

Drawing of the description:

To get the total area, we have to calculate the area of the rectangle and trapezoid, and then add them.

• Area of rectangle

$A_r=b\times h$$A_r=30\times12=360ft^2$

• Area of trapezoid

$A_t=\frac{1}{2}h\cdot(b_1+b_2)$$A_t=\frac{1}{2}\cdot15\cdot(30+15)=\frac{15}{2}\cdot(45)=337.5ft^2$

• Area of the front of the house

Finally, to get the total area we add them:

$A_T=360+337.5=697.5ft^2$

Answer: 697.5 ft²