Question

In the given rectangle PQRS as shown,
The area of the right angle triangle PQS is ____ ft.

• A. 32
• B. 36
• C. 42
• D. 48

Answer 1

The correct option is D 48

From the rectangle PQRS,
Length(l) = 12 ft
Breadth(b) = 8 ft

$\text{Area of rectangle PQRS =}l\times b$
$=12\times 8$
$=96\text{sq.ft}$

Let the area of right angle triangle PQS be ${}^{\prime }{y}^{\prime }ft$.

We know,
Diagonal divides the rectangle into two equal/congruent right angle triangles.
i.e
Area of triangle PQS + Area of triangle PQS = Area of rectangle PQRS

$\Rightarrow y+y=96$
$\Rightarrow 2y=96$

$\text{Area of triangle PQS}\Rightarrow y=48\text{sq.ft}$