Question

What is the surface area of a regular square pyramid with a slant height of 12 cm and a lateral edge of 13 cm?

Answer 1

240in^2

Explanation:

Answer 2

Look at the picture.
Use the Pythagorean theorem:

`\left((1)/(2)b\right)^2+12^2=13^2\\\\(1)/(4)b^2+144=169\ \ \ |-144\\\\(1)/(4)b^2=25\ \ \ |\cdot4\\\\b^2=100\to b=√(100)\to b=10\ cm`
The area of the triangle:

`A_t=(10\cdot12)/(2)=60\ cm^2`
The area of the square:

`A_s=10^2=100\ cm^2`
The surface area of rectangular square pyramid:

`SA=4A_t+A_s\\\\SA=4\cdot60+100=340\ cm^2`