Answer:
952 ft²
Step-by-step explanation:
The total surface area is the sum of the areas of the various faces.
List of faces
The area is the sum of ...
bottom + (yellow) front square + (yellow) back square + ...
(yellow) left rectangle + (yellow) right rectangle + ...
(white) front triangle + (white) back triangle + ...
(white) left rectangle + (white) right rectangle
Recognizing that front/back and left/right parts have the same area, we can compute one of them and multiply by 2.
Triangle area
The area of a triangle is given by the formula ...
A = 1/2bh
The triangles shown have a base of 10 ft and a height of 8 ft, so their area is ...
A = 1/2(10 ft)(8 ft) = 40 ft²
Rectangle area
Ignoring the front and back squares, there are three rectangles we need to find the areas of. The area formula in each case is ...
A = LW
bottom area = (10 ft)(14 ft) = 140 ft²
(yellow) right rectangle = (14 ft)(10 ft) = 140 ft²
(white) right rectangle = (14 ft)(9 ft) = 126 ft²
Square
The area of the front and back squares is the square of their side lengths:
A = s² = (10 ft)² = 100 ft²
Total area
Using the above list, we find the total surface area to be ...
total = (bottom) 140 ft² + (squares) 2×100 ft² + ...
(yellow left/right) 2×140 ft² + ...
(white triangles) 2×40 ft² + ...
(white left/right) 2×126 ft²
total = (140 +2(100 +140 +40 +126)) ft² = (140 +2(406)) ft² = 952 ft²
The surface area of the composite figure is 952 square feet.
