Chapter 12, Problem 5MCQ

To determine

To calculate : The lateral area of the prism.

Answer to Problem 5MCQ

The lateral area of the prism would be $257c{m}^2$

Explanation of Solution

Given information : A triangular prism is given base sides are 7 cm and 8 cm with a height of 10 cm.

  

Formula used : The lateral surface area of the triangular prism is $ph$ . And the slant side is $l=\sqrt{a^2+b^2}$ . Where $p$ is the perimeter of the base and $h$ is the height of the prism and $a$ , $b$ are the base sides. And the perimeter will be the sum of the base sides.Calculation : Calculate the slant height.

  $l=\sqrt{a^2+b^2}$

  $\begin{array}{l}l=\sqrt{7^2+8^2}\\ l=\sqrt{49+64}\\ l=10.7cm\end{array}$

Now, calculate the perimeter of the base

  $\begin{array}{l}p=a+b+l\\ p=7+8+10.7\\ p=25.7cm\end{array}$

Calculating the lateral surface area now.

  $\begin{array}{l}L=ph\\ L=25.7\times 10\\ L=257c{m}^2\end{array}$