Question

A square pyramid and a cube have the same surface area don’t of each side of the base of the Square pyramid is 10 feet the width of the cube is 6 feet what is the lateral height of the square pyramid

Answer 1

Answer:

The lateral height of the square pyramid is $5.8\ ft$

Step-by-step explanation:

step 1

Find the surface area of the cube

The surface area of the cube is equal to

$SA=6b^{2}$

where

b is the length side of the cube

w have

$b=6\ ft$

substitute

$SA=6(6^{2})=216\ ft^{2}$

step 2

Find the lateral height of the square pyramid

we know that

the surface area of the square pyramid  is equal to

$SA=B+4(\frac{1}{2}bh)$

where

B is the area of the base

b is the base of the lateral triangle (base of the square)

h is the lateral height of the square pyramid

$B=(10^{2})=100\ ft^{2}$

$SA=216\ ft^{2}$ -----> is the same surface that the cube

$b=10\ ft$

substitute the values and solve for h

$216=100+4(\frac{1}{2}*(10)*h)$

$216-100=20h$

$h=116/20=5.8\ ft$