Question

The pyramid of the sun in mexico is a square pyramid. the base edge is approximately 220 meters, and the height is approximately 70 meters. what is the approximate surface area of the sides of the pyramid to the nearest thousand square meters? the lateral surface area is about .

Answer 1

The lateral surface area is about 105,600 meters.

What is lateral area of ​​a pyramid?

The area of ​​the pyramid is the measure relative to its surface and is obtained by the sum of the areas of the bases (polygonals) and of all the lateral faces (triangles). For the calculation of the lateral area of ​​a pyramid, we will have the perimeter of the base by the inclined height of the pyramid.

In this case, the formula of the lateral surface area is:

$SA=\frac{P*S}{2}+B$

Where:

• P= perimeter of base
• S= slant height
• B= area of base

The height informed will not be used, it will only be a parameter to perform pythagoras, that is, we will find the hypotenuse of the triangle created by the height, like this:

$S=\sqrt{(B)^2/2+H^2} \\S=\sqrt{110^2+70^2}\\S=\sqrt{17,000}\\ S=130$

Returning to the formula given above, we find that:

$SA= \frac{(220*4)(130)}{2}+(220*220)\\ SA= 57,200+48,400= 105,600 \ meters$

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