Question

Explain how you could calculate the surface area of a square pyramid.

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Answer 1

The steps below are used to compute the surface area of a square pyramid.

Step 1: Given data

length of base of square pyramid$=a$

slant height of square pyramid$=l$

Height of square pyramid$=h$

surface area of square pyramid $=?$

Step 2: Calculating the surface area of square pyramid

Area of the base of square pyramid will be equal to area of square$=a^{2}$

Area of the four triangular faces$=2\times a\times l$

Also, in case slant height, $l$ is not given, we can calculate it using height, $h$.

$l=\sqrt{\frac{a^{2} }{4}+h^{2} }$

Now, adding all the areas to calculate the total surface area of square pyramid.

Total surface area$=$ area of base $+$ area of four triangular faces

Total surface area$=a^{2}+2al= a^{2}+2a\times\sqrt{\frac{a^{2} }{4}+h^{2} }$

Thus, the surface area of a square pyramid is $a^{2}+2a\times\sqrt{\frac{a^{2} }{4}+h^{2} }$.

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Answer 2

Answer:

Sample response: You would first calculate the area of the base, which is length times width. You would then calculate the area of the faces, which is 1 2 (base times height) and multiply the result by 4 for the 4 faces. Finally, add the area of the base and the areas of the faces.

Step-by-step explanation: sample response on edge 2022