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Naddika [18.5K]
3 years ago
13

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
Mathematics
1 answer:
o-na [289]3 years ago
6 0

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

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