Question

Which of the following are true for the parallelogram given below with dimensions 17 cm$\times$ 15 cm?

• A. $h=\sqrt{116}$ m
• B. $h=\sqrt{187}$ m
• C. Area = 255 $m^2$
• D. Area = 183$m^2$

Answer 1

Answer: (A), (D)

The correct options are
A $h=\sqrt{116}$ m
D Area = 183$m^2$

Consider the parallelogram ABCD.
Since opposite sides are equal, we have AB = CD and AD = BC.
Consider $△ADE.$
Using Pythagoras' theorem,
we get
$A{D}^2=A{E}^2+D{E}^2.$
${15}^2=h^2+3^2$
$\Rightarrow h^2={15}^2-3^2$
$=225-9$
$\Rightarrow h^2=116c{m}^2$
$\therefore h=10.77cm$
Area of a parallelogram is the product of its base and corresponding height.
$\Rightarrow \text{Area}=h\times DC=10.77\times 1\approx 183{\text{cm}}^2$