Question

the question is in the picture ​

Answer 1

$\huge{\mathcal{\blue{\underline{Answer}}}}$

first we have to find The length of the base of the right angled triangle to find its area :

$bc {}^{2} = ce {}^{2} + eb {}^{2} \\ (10cm) {}^{2} = (8cm) {}^{2} + cb {}^{2} \\ 100cm {}^{2} = 64cm {}^{2} + eb {}^{2} \\ 100cm {}^{2} - 64cm {}^{2} = eb {}^{2} \\ 36cm {}^{2} = eb {}^{2} \\ \sqrt{36cm {}^{2} } = eb$

$\huge{\mathcal{\blue{\underline{6cm=EB}}}}$

The area of the right angled triangle ∆CEB :

$= \frac{1}{ 2} \times base \times hieght \\ = \frac{1}{2} \times (ce) {}^{2} + ( eb) {}^{2} \\ = \frac{1}{2} \times (6cm) \times (8cm) \\ = 24cm {}^{2}$

now the area of the rectangle ABCD :

$= length \times breath \\ = 18cm \times 10cm \\ = 180cm {}^{2}$

Area of the of the shaded region(ADCEB)

= area of rectangle - area of triangle

$= 180cm {}^{2} - 24cm {}^{2} \\ = 156cm {}^{2}$

Answer 2

Answer:

By Pythagoras theorem,

Hypotenuse ² = Base² + Height ²

=> 10² = EB² + 8²

=> EB²= 10² -8²

=> EB²= 100 - 64

=> EB²= 36

=> EB = sq. root of 36

=> EB = 6 cm

Area of a triangle = 1/2 × base × height

=> 1/2 × 6×8

=>24 cm²

Area of the rectangle = length × breadth

=> ( 18 × 10 ) cm²

=> 180 cm²

Area of the shaded region = (180 - 24 ) cm²

=> 156 cm²