Question

the surface area of a rectangular prism is 136 square centimeters. If the length is 8 centimeters and the width is 4 centimeters, calculate the height of the prism.

Answer 1

we know that rectangular prism means a cuboid.

therefore the surface area of the cuboid is 136cm²

given :-

length of the cuboid = 8cm

breadth of the cuboid = 4cm

height of the cuboid = ?

we know the formula for solving for the TSA of the cuboid, that is 2 ( lb + bh + lh )

therefore 2 ( lb + bh + lh ) = 136cm²

==> [ ( 8 × 4 ) + ( 4 × h ) + ( 8 × h ) = 136/2

==> ( 32 + 4h + 8h ) = 68

==> 32 + 12h = 68

==> 12h = 68 - 32

==> 12h = 36

==> h = 36/12

==> h = 3

hence, the height of the cuboid (rectangular prism) is 3cm.

HOPE THIS HELPS..!!

Answer 2

Hello!

• Length = $\bf{8\:cm}$
• Breadth = $\bf{4\:cm}$

Then,

$\sf Surface \:area\:of\:Cuboid = 136\:cm^{2} \\ \\ \implies \sf 2(lb+bh+hl) = 136 \\ \\ \implies (8\times4)+(\sf 4\times h)+(\sf 8\times h) = \dfrac{136}{2} \\ \\ \implies \sf 32 +4h+8h = 68 \\ \\ \implies \sf 32+12h = 68 \\ \\ \implies \sf 12h = 68-32 \\ \\ \implies \sf h = \dfrac{36}{12} \implies \boxed{\red{\bf{h = 3 \:cm}}}$

Cheers!