Question

find the area of the shaded portion in the given figure.​

Answer 1

Given:-

• A rectangle ABDF.

To Find:-

• Area of the shaded portion

Formula Used:-

• ${\boxed{\bf{\red{Area\:of\:Rectangle = Length \times Height}}}}$

• ${\boxed{\bf{\red{Area\:of\:Triangle = \dfrac{1}{2}\times Base \times Height}}}}$

Solution:-

Firstly,

$\sf :\implies Area\:of\:Rectangle\:ABDF = Length \times Height$

$\sf :\implies Area\:of\:Rectangle\:ABDF = 5 \times 8$

$\sf :\implies Area\:of\:Rectangle\:ABDF =40\:cm^2$

Now,

$\sf :\implies Area\:of\:Triangle\:GEF = \dfrac{1}{2}\times Base \times Height$

$\sf :\implies Area\:of\:Triangle\:GEF = \dfrac{1}{2}\times 6 \times 3$

$\sf :\implies Area\:of\:Triangle\:GEF = 3\times 3$

$\sf :\implies Area\:of\:Triangle\:GEF = 9\:cm^2$

And,

$\sf :\implies Area\:of\:Triangle\:CED = \dfrac{1}{2}\times Base \times Height$

$\sf :\implies Area\:of\:Triangle\:CED = \dfrac{1}{2}\times 2 \times 4$

$\sf :\implies Area\:of\:Triangle\:CED =2 \times 2$

$\sf :\implies Area\:of\:Triangle\:CED = 4\:cm^2$

Finally,

$\sf :\implies Area\:of\: Shaded\: Portion =Area\:of\:Rectangle\:ABDF - [Area\:of\:Triangle\:GEF + Area\:of\:Triangle\:CED]$

$\sf :\implies Area\:of\: Shaded\: Portion =40 - [9 + 4]$

$\sf :\implies Area\:of\: Shaded\: Portion =49 - 13$

$\sf :\implies Area\:of\: Shaded\: Portion =36\:cm^2$

Hence, The Area of the Shaded Portion is 36 cm².

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