Use these formulas to help solve the problem.

Question

​ Area of a Triangle; A = ½bh​

Area of a Rectangle; A = lw

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​The front view of a house is composed of a triangle and a rectangle.

​The picture shows the front view of a house.

The picture depicts a triangle with a right angle in the middle with the word 10 feet. Then contected to it is a sqare making the shape of the a house. It has the width of 24 and the length of 20 feet.

What is the area of the front of the house in square feet?



Type in your final answer (number only) in the box below.

(1 point)
Area =
square feet
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Answer 1

To find the total area of the front of the house, we need to calculate the area of both the triangle and the rectangle and then add them together.

1. Area of the Triangle:

   • We know that the height (h) of the triangle is 10 feet.
   • The base (b) of the triangle can be inferred from the width of the house, which is 24 feet.
   • Using the formula for the area of a triangle: \[ A = \frac{1}{2}bh \] Substituting the values: \[ A = \frac{1}{2} \times 24 \times 10 = \frac{1}{2} \times 240 = 120 \text{ square feet} \]

2. Area of the Rectangle:

   • The length (l) is 20 feet and the width (w) is 24 feet.
   • Using the formula for the area of a rectangle: \[ A = lw \] Substituting the values: \[ A = 20 \times 24 = 480 \text{ square feet} \]

3. Total Area of the Front of the House:

   • Now, we add the area of the triangle and the rectangle: \[ \text{Total Area} = \text{Area of Triangle} + \text{Area of Rectangle} = 120 + 480 = 600 \text{ square feet} \]

Thus, the total area of the front of the house is:

600 square feet