Question

In the following figures find the area of shaded regions

Answer 1

$\bf{\underline{To\:Find:-}}$

Area of the shaded figure.

$\bf{\underline{Given:-}}$

PQRS is a square with side 20 cm

$\bf{\underline{Solution:-}}$

Side of square = 20 cm

$\sf{Area = (side)^2 \:sq.units}$

$\sf{Area = (20)^2 \:cm^2}$

$\sf{Area = 400\:cm^2}$

Now,

In ∆SLR,

SL = 10 cm

SR = 20 cm

$\sf{Area = \dfrac{1}{2}\times base \times height}$

= $\sf{Area = \dfrac{1}{2}\times 10\times 20}$

= $\sf{Area = 100\: cm^2}$

Now,

In ∆PLM,

PM = 10 cm

PL = 10 cm

$\sf{Area = \dfrac{1}{2}\times10\times10}$

= $\sf{Area = 50\:cm^2}$

Now,

In ∆QMR,

QM = 10 cm

QR = 20 cm

$\sf{Area = \dfrac{1}{2}\times10\times20}$

= $\sf{Area = 100\:cm^2}$

Now,

Total Area of three Triangles:-

= $\sf{(100+50+100)\:cm^2}$

= $\sf{250\:cm^2}$

Therefore,

Area of shaded region = Area of square - Total Area of the three Triangles.

= $\sf{Area\:of\:shaded\:region = (400 - 250)\:cm^2}$

= $\sf{Area\:of\:Shaded\:region = 150\:cm^2}$

$\bf{\underline{Additional\:Information}}$

• $\sf{Area\:of\:square=(side)^2\:\:sq.units}$
• $\sf{Area\:of\:triangle=(\dfrac{1}{2}\times base\times height)\:\:sq.units.}$