Pyramids: by this smart lady in Arizona

Geometry Level 3
  1. Each side of the square pyramid shown below measures 10 inches. The slant height, H, of this pyramid measures 12 inches.

A. What is the area, in square inches, of the base of the pyramid?

B. What is the total surface area, in square inches, of the pyramid?

A. 100 inches squared B. 100+4 (1/2) 12*10 = 340 inches squared A. 101 inches squared B. 107+3 (1/2) 12*11= 370 inches squared A. 102 inches squared B. 110+5 (1/2) 11*14 = 312 inches squared A. 103 inches squared B. 101+2 (1/2) 12*20 = 411 inches squared

Jessica Frank by Jessica Frank , 92, USA

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1 solution

Base of the pyramid is a square with side length = 10 inches

We know that,

Area of square = (side length)²

So,

Area of base = 10×10 inches = 100 s q u a r e i n c h e s \boxed{100 square inches}

The problem is over here because if you observe the options, only third option have 100 square inches as the answer. So, third option is the correct one. But if you want to solve the second part here it is:-

H = slant height = 12 inches

B = base lenght = 10 inches

h = perpendicular height = H ² − B ² \sqrt{H² - B²} = 44 \sqrt{44}

Surface area of a Square Pyramid = B² + 2B B ² 4 + h ² \sqrt{\frac{B²}{4} + h²}

After solving,

Surface area of the pyramid = 340 s q u a r e i n c h e s \boxed{340 square inches}

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