Question

Given, ABCD is a square; the sides
AD = 5 cm
AP = 1 cm
CR = 1 cm
Find the area of $\Delta PQR$

• A. $2c{m}^2$
• B. $7c{m}^2$
• C. $7.5c{m}^2$
• D. $8c{m}^2$

Answer 1

The correct option is C

$7.5c{m}^2$

Here PQ is the height QR is the base.
Since the side of the square is given as 5 cm
$\therefore$BC = 5 cm and PQ = AB = 5 cm
QR = BC - (BQ + CR)
BQ = AP = 1 cm
Hence
QR = 5-[1+1]
= 5 - 2
= 3 cm

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

Area of triangle PQR $=\frac{1}{2}\times QR\times PQ$
$=\frac{1}{2}[3\times 5]$
$=\frac{15}{2}$
$=7.5c{m}^2$