Question

Select the correct answer.

A model of Steven’s house is shown in the diagram. He is replacing the roof, which consists of two rectangular surfaces. The diagram shows one side of the roof, with the other side hidden from view. What is the total area of the roof to the nearest square foot?

Answer 1

Answer:

Option B

Step-by-step explanation:

From the picture attached,

Area of the one side of the roof = Area of the rectangle

                                                     = Length × Width

                                                     = AE × AC

To get the length of side AC, construct a perpendicular AD on side BC which divides BC in two equal parts.

BD = DC = 13 ft

By applying cosine rule in ΔADC,

cos(45)° = $\frac{\text{DC}}{\text{AC}}$

$\frac{1}{\sqrt{2}}=\frac{13}{\text{AC}}$

AC = 13√2

AC = 18.38 ft

Therefore, area of one side of the roof = 38 × 18.38

                                                                 = 698.62 square feet

Area of both the sides of the roof = 698.62 × 2

                                                        = 1397.24 feet²

                                                        ≈ 1397 feet²

Option B will be the answer.

Answer 2

The total area of the roof to the nearest square foot is 1,397 square feet

Area of composite shapes.

In order to get the area of the roof, we will need the slant height of the triangle.

Using the pythagoras theorem;

$cos45 = \frac{26/2}{l} \\cos 45 = \frac{13}{l} \\0.7071 = \frac{13}{l} \\l = \frac{13}{0.7071} \\l=18.39 feet$

Get the area of the roof

Area of the roof = 2(lw)

• l is the length of the rectangle = 38ft
• w is the width  = 18.39 feet

Area of the roof = 2(38 * 18.39)

Area of the roof = 1,397.64

Area of the roof ≈ 1,397 square feet

Hence the total area of the roof to the nearest square foot is 1,397 square feet

Learn more on area of rectangle here: https://brainly.com/question/25292087