Question

find the area shaded portion as shown in the following picture ​

Answer 1

Required to find :-

• Area of the shaded portion ?

Formulae used :-

$\leadsto{\boxed{\tt{ Area \; of \; a \; parallelogram = base \times height }}}$

$\leadsto{\boxed{\tt{ Area \; of \; a \; triangle = \dfrac{1}{2} \times base \times height }}}$

Solution :-

The given 2nd geometrical figure is called as parallelogram .

In which the shaded part is in the shape of a rectangle and the left unshaded part is the 2 right-angled triangles !

And ,

Similarly, we were given with some measurements ;

They are namely ;

• Base of the parallelogram = 90 cm

• Height of the parallelogram = 30 cm

( Here , height is the the line which is perpendicular to the base )

We need to find the area of the shaded part ( that is rectangle )

So,

we can solve this using 2 methods !

But I am going to tell the lengthy method because it is easy to remember .

Here,

We need to use the trick that is ,

Area of the parallelogram = Area of the 2 right-angled triangles + Area of the rectangle

Since,

we want to find the area of the rectangle .

Hence,

The formula becomes as ;

Area of the rectangle = Area of the parallelogram - Area of the 2 right-angled triangles

So,

Dimensions of a parallelogram

• Base = 90 cm

• Height = 30cm

Using the formula ;

$\leadsto{\boxed{\tt{ Area \; of \; a \; parallelogram = base \times height }}}$

So,

$\rightarrowtail{\rm{\large{area \: = 90 \: cm \times 30 \: cm}}}$

$\rightarrowtail \large \rm area \: = 2700 \: {cm}^{2}$

Hence,

Area of the parallelogram = 2,700 cm²

Similarly,

Dimensions of the triangle

( Here both triangles have equal sides )

So,

Area of 1st triangle = Area of 2nd triangle

Hence,

Area of the 2 triangles = ?

Dimensions

• Base = 10 cm

• Height = 30 cm

using the formula ,

$\leadsto{\boxed{\tt{ Area \; of \; a \; triangle = \dfrac{1}{2} \times base \times height }}}$

So,

$\leadsto \tt \large \: area = 2 \times \dfrac{1}{2} \times 10 \times 30$

$\leadsto \tt \large area \: = 2 \times \: 5 \times 30$

$\leadsto \tt \large area \: = 300 \: {cm}^{2}$

Hence,

Area of the 2 right-angled triangles = 300 cm²

This implies ,

Area of the rectangle = Area of the parallelogram - Area of the 2 triangles

So,

Area of the rectangle = 2700 cm² - 300 cm²

=> Area of the rectangle = 2,400 cm²

Therefore ;

Area of the rectangle = 2,400 cm²

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Area\:of\:shaded\:region=2400\:cm^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Height \: of \: parallelogram = 30 \: cm \\ \\ \tt: \implies Base \: of \: parallelogram = 90 \: cm \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Area \: of \: shaded \: region =?$

• According to given question :

$\tt \circ \: \triangle \: ABC = \triangle \: DE F \\ \\ \tt \circ \: DE = 10 \:cm \\ \\ \tt \circ \: CD = 80 \: cm \: \: \: \: (Length) \\ \\ \tt \circ \: Breadth = 30 \: cm \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: rectangle = l \times b \\ \\ \tt: \implies Area \: of \: rectangle =80 \times 30 \\ \\ \green{\tt: \implies Area \: of \: rectangle =24000 { \: cm}^{2} } \\ \\ \green{\tt \therefore Area \: of \: shaded \: region \: is \: 2400 \: {cm}^{2} }$