Question

What is the surface area of a square pyramid that has a side length of 5 inches and a slant height of 6 inches?

25 in.2
96 in.2
60 in.2
85 in.2​

Answer 1

85 in² hope that helps <3

Answer 2

The surface area of the square pyramid is 85
`\text { inches }^(2)`

Solution:

We have been given the dimension of a square pyramid with a side length of 5 inches and a slant height of 6 inches

We need to find the surface area of this square pyramid.

A square pyramid is a three-dimensional figure with a square base and 4 triangles forming a dome over it.

So, to find the surface area of a square pyramid we can use the following formula:

`\text {Area of a square pyramid }=a^(2)+2 a \sqrt{(a^(2))/(4)+h^(2)}`

Where “a” is the base length and "h" is the height of the pyramid.

But we need to find the height of the triangle. This can be done using Pythagoras theorem.

We only use half the base in Pythagoras theorem to find the height.

Therefore,

`\begin{array}{l}{\text { Hypotenuse }^(2)=\text { base }^(2)+\text { height }^(2)} \\\\ {6^(2)=(2.5)^(2)+h^(2)} \\\\ {36-6.25=h^(2)} \\\\ {h=√(29.75)} \\\\ {h=5.45 \text { inches. }}\end{array}`

So now, the area of the square pyramid is:

`=5^(2)+2(5) \sqrt{(5^(2))/(4)+5.45^(2)}`

`\begin{array}{l}{=25+10 \sqrt{(25)/(4)+29.7025}} \\\\ {=85 \text { inches}^(2)}\end{array}`

Thus surface area of square pyramid is 85
`\text { inches }^(2)`