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A child's toy is in the shape of a square pyramid. The pyramid stands 20 inches tall and each side of the base measures 24 inches.

Half of the surface area of the pyramid is black and the remainder is yellow.

What is the surface area of the toy that is yellow?

User Jishnu A P
by
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1 Answer

7 votes

Answer: 1704 square inches

Explanation:

The surface area of a square pyramid is given by the formula:

Surface Area = base area + 4 × (1/2 × slant height × base length)

The base area of the pyramid is:

base area = length × width = 24 in × 24 in = 576 in²

The slant height of the pyramid can be found using the Pythagorean theorem:

slant height = sqrt(20² + 12²) = 236/5 in

Therefore, the surface area of the whole pyramid is:

Surface Area = 576 in² + 4 × (1/2 × 236/5 in × 24 in) = 1152 in² + 2256 in² = 3408 in²

Half of this area is black, so the area that is yellow is:

Yellow Area = 1/2 × 3408 in² = 1704 in²

Therefore, the surface area of the toy that is yellow is 1704 square inches.

User OliverRadini
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