Question

Solve for the surface area of the square pyramid illustrated below where h is the
height and s is the edge of the base.
h=5m
s=10m
1. 100 m2
B. 150 m2
C. 200 m2
D. 250 m2​

Answer 1

Answer:

c) 200m2

Step-by-step explanation:

1. SA= 2bs + b^2
2. SA=2(10)(5) + (10)^2
3. SA=100 + 100
4. SA=200m2

Answer 2

Given,

A Square Pyramid with height h = 5m and edge s = 10m.

To Find,

The surface area of the square pyramid.

Solution,

The surface area of the pyramid is equal to the sum of areas of all the 4 triangular sides with the base area.

The formula for the surface area of a pyramid, when edge and height are given is $s^{2}+2s\sqrt{\frac{s^{2} }{4}+h^{2} }$, where $s =$ edge and $h =$ height

From the given data $s$ = 10m and $h$ = 5m

Thus surface area of the pyramid = $10^{2}+2(10)\sqrt{\frac{10^{2} }{4}+5^{2} }$

= $100 + 20 \sqrt{\frac{100 }{4}+25 } = 100 + 20\sqrt{50} = 100+20(7.071) = 241.421$

Thus in the given options, the nearest value for the above-calculated area is 250 $m^{2}$

Henceforth, the surface area of the pyramid is 250 $m^{2}$.