Question

A right triangular prism has a height of $26\mathrm{cm}$ and base edges of $10\mathrm{cm},24\mathrm{cm},$ and $26\mathrm{cm}$.

What is the lateral area of the prism?

• A. $1560{\mathrm{cm}}^2$
• B. $1680{\mathrm{cm}}^2$
• C. $800{\mathrm{cm}}^2$
• D. $3120{\mathrm{cm}}^2$

Answer 1

The correct option is A

$1560{\mathrm{cm}}^2$

Explanation for correct option :

Step-1 : Dimension of lateral faces.

Given height of right triangular prism $26\mathrm{cm}$ and base edges of $10\mathrm{cm},24\mathrm{cm},$ and $26\mathrm{cm}$
There are three lateral faces of dimension ;
$$\begin{gathered} {\mathrm{D}}_1=24\mathrm{cm}\times 26\mathrm{cm} \\ {\mathrm{D}}_2=10\mathrm{cm}\times 26\mathrm{cm} \\ {\mathrm{D}}_3=26\mathrm{cm}\times 26\mathrm{cm} \end{gathered}$$
Here ${\mathrm{D}}_1,{\mathrm{D}}_2\hspace{0.17em}\&{\mathrm{D}}_3$ are the dimension of three lateral faces

Step-2 : Area of lateral faces :

Let the area of three lateral faces is ${\mathrm{A}}_1,{\mathrm{A}}_2\&{\mathrm{A}}_3$.
$$\begin{gathered} {\mathrm{A}}_1=24\times 26 \\ =624{\mathrm{cm}}^2 \\ {\mathrm{A}}_2=10\times 26 \\ =260{\mathrm{cm}}^2 \\ {\mathrm{A}}_3=26\times 26 \\ =676{\mathrm{cm}}^2 \end{gathered}$$
Total area of lateral faces $={\mathrm{A}}_1+{\mathrm{A}}_2+{\mathrm{A}}_3$
$$\begin{gathered} =624+260+676 \\ =1560{\mathrm{cm}}^2 \end{gathered}$$

Hence, option $A$ is correct.