Question

Calculate the surface area of the solid shown in the figure excluding the bottom surface :

• A. 1227.40
• B. 1223.60
• C. 1323.60
• D. 1000.36

Hint:

Split the solid into a 10 x 10 x 20 box and a triangular wedge, then add the areas of all exposed faces except the base.

Answer 1

The Correct Option is C

Reading the figure: the solid is a square-based block (10 x 10 base, height 20) with a wedge attached to one side. The wedge is 10 wide, its back edge is 20 high and its front edge is at ground level, so its slanted top face runs from the top back edge down to the ground.
Exposed faces (bottom excluded):
Top of the block: 10 x 10 = 100
Two side faces and the back face of the block: 3 x (10 x 20) = 600
Remaining triangle on the block's face next to the wedge (base 10, height 20): (1/2) x 10 x 20 = 100
Back face of the wedge: 10 x 20 = 200
Triangular end face of the wedge: (1/2) x 10 x 20 = 100
Slanted face of the wedge: 10 x √(10² + 20²) = 10 x 22.36 = 223.60
Total = 100 + 600 + 100 + 200 + 100 + 223.60 = 1323.60
Answer: (3) 1323.60