Question

This image shows a square pyramid. What is the surface area of this square pyramid? 36 ft² 72 ft² 78 ft² 84 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 6 feet. The lateral edge makes a 45 degree angle with the base edge.

Answer 1

72

Explanation:

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Answer 2

the picture in the attached figure

we know that
In a square pyramid we have five faces, 4 triangles and 1 square. So to determine surface area we need to take the areas of the triangles and square and add them all up

The square's area is relatively simple:A=b²
A=6²=36 ft²But now let's observe the triangles, a triangle's area is:
A=(1/2)*b*hthe base is equal to 6 ftb=6 ftAC=BC----------> because the angle is 45°AC=6 ft/2----> 3 ftsoBC=3 ftA=(1/2)*6*3----> 9 ft²
Multiply the triangle's area by four to account for all four triangular faces and add the squares area for your answer
Surface area=36 +4*9-----> 72 ft²the answer is
72 ft²