Question

What is the surface area of the figure shown?

Answer 1

The total area of the composite figure is 434 square ft

Calculating the area of the figure

From the question, we have the following parameters that can be used in our computation:

The composite figure

The total area of the composite figure is the sum of the individual shapes

Where, we have the following shapes and dimensions:

• Rectangle: 16 ft by 7 ft and 13 ft by 16 ft
• Trapezoid: Parallel sides: 7 ft and 12 ft, Height: 12 ft

Using the area formulas (Length * Width for Rectangles), we have the following:

• Rectangles: 16 * 7 + 13 * 16 = 320
• Trapezoid = 1/2 * (7 + 12) * 12 = 114

Add up the individual areas

Area = 320 + 114

Evaluate the expression

Surface area = 434

Hence. the total area of the figure is 434 square ft

Answer 2

The surface area of the figure = 962 ft²

Explanation:

The rectangle dimensions and its area given below

Dimensions Number Area

12 x 7 2 12 x 7 x 2 = 168

16 x 7 1 16 x 7 = 112

12 x (16 + 5) 1 12 x 21 = 252

16 x 12 1 16 x 12 = 192

16 x 13 1 16 x 13 = 208

Triangle dimensions

Dimensions Number Area

b = 12 & h = 5 2 bh/2 = (12*5)/2 = 30

To find total area

Total area = 168 + 112 + 252 + 192 + 208 + 30 = 962 ft²