Question

Find the area of the unfolded envelope as shown in the given figure.

• A. $48\text{sq. in}$
• B. $40\text{sq. in}$
• C. $98\text{sq. in}$
• D. $88\text{sq. in}$

Answer 1

The correct option is D $88\text{sq. in}$

Divide the entire envelope into the following figures:


Area of the unfolded envelope = Area of Figure I + Area of Figure II + Area of Figure III

Now, Figure I and III are triangles and Figure II is a rectangle.

$\text{Area of triangle}=\frac{1}{2}\times \text{height}\times \text{base}$


$\text{So, area of Figure I}=\frac{1}{2}\times \text{base}\times \text{height}$
$=\frac{1}{2}\times 8\times 6$
$=24\text{sq. in}$

Figure I and III have same height and base.

∴ Area of Figure I = Area of Figure III = 24 sq. in.

Now, area of rectangle = length × width

So, area of Figure II = length × width
$=8\times 5$
$=40\text{sq. in}$

Area of the unfolded envelope will be:
$=24+24+40$
$=88\text{sq. in}$