The base of the pyramid is a square what is the surface area if the pyramids height is 4 feet in the area of the base is 36 ft.?

Mathematics

1 answer:

KATRIN_1 [288]3 years ago

8 0

Answer:

96 ft²

Step-by-step explanation:

The general formula for the surface area of a pyramid is:

SA = $\frac{1}{2}$ pl + B, were p = the perimeter of the base, l = the slant height and B = the area of the base

Since the area of the base is 36 ft², then each side is √36, or 6 ft. The perimeter is the sum of all the sides, so 6 x 4 = 24 ft.

Given the overall height of the pyramid is 4 feet, you can use the Pythagorean Theorem (a² + b² = c²) to find the slant height (hypotenuse) of the pyramid. Using 3 feet for 'a' and 4 feet for 'b':

3² + 4² = c² or 9 + 16 = 25

25 = c² or c = 5

SA = $\frac{1}{2}$ (24)(5) + 36

SA = 60 + 36 = 96 ft²

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Step-by-step explanation:

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