Question

What is the slant height of a square pyramid that has a surface area of 189 square feet and a side length of 7 feet?

Answer 1

10..............................

Answer 2

Answer: The slant height of a square pyramid is 10 feet.

Explanation:

Since we have given that

Surface area of square pyramid = 189 square feet

Length of side of square = 7 feet

Area of base will be given by

`Side* Side=Side^2=7^2=49\ ft^2`

Let 'l' be the slant height of the square pyramid.

As we know that "Formula for surface area of square pyramid" is given by

`\text{Surface area}=\text{Area of base}+(1)/(2)* \text{Perimeter of square}* l\\\\189=7^2+(1)/(2)* 4* 7* l\\\\189=49+14l\\\\189-49=14l\\\\140=14l\\\\(140)/(14)=l\\\\10\ feet=l`

Hence, the slant height of a square pyramid is 10 feet.