Question

If the total area of the given figure is 662 sq. in, find the value of unknown length 'y' (in inches).

• A. 8
• B. 9
• C. 12
• D. 6

Answer 1

The correct option is B 9

The given figure consist of one rectangle and two similar right angle triangles.


Hence,
Total area = Area of rectangle ABGH + Area of triangle BCD + Area of triangle EFG

$\text{Area of rectangle ABGH = length}\times \text{width}$
$=20\times 25$ $=500\text{sq. in}$

$\text{Area of}\Delta \text{BCD = Area of}\Delta \text{EFG}$
$=\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times y\times 18$

So,
$662=500+2\times \frac{1}{2}\times y\times 18$

$662-500=y\times 18$

$162=y\times 18$

$\frac{162}{18}=y$

$\therefore y=9\text{in}$