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This image shows a square pyramid. What is the surface area of this square pyramid?

25 ft²
100 ft²
125 ft²
200 ft²
Note: Image not drawn to scale. The figure shows a square pyramid. The slant height is shown as a dashed line perpendicular to the base edge. The length of the base edge is 10 feet. The lateral edge makes a 45 degree angle with the base edge.

User SPRBRN
by
6.1k points

2 Answers

5 votes

Answer:

200
ft^(2)

Explanation:

User Terman
by
6.1k points
7 votes

Answer:

200 ft²

Explanation:

Each face is an isosceles right triangle with a hypotenuse of length 10 ft. The area of each of those triangles is

A = 1/4·h² . . . . where the h in this formula is the hypotenuse length

So, the area of the four faces (the lateral area of the pyramid is 4 times this, or ...

A = 4·1/4·(10 ft)² = 100 ft²

Of course, the base area is simply the area of the square base, the square of its side length:

A = (10 ft)² = 100 ft²

So, the total area is the sum of the lateral area and the base area:

total area = 100 ft² +100 ft² = 200 ft²

_____

If you think about this for a little bit, you will realize the pyramid must have zero height. That is, the slant height of a face is exactly the same as the distance from the center of an edge to the center of the base. "Not drawn to scale" is a good description.

User Rafael Borja
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6.1k points