Question

In the adjoining figure,ABCD is a rectangle in which AB=18 cm,BC=8 cm and DE=10cm. Find the area of the shaded region EBCD.​

Answer 1

From the given figure, AD=8cm, DE=10 cm, CB=10 cm and AB=18 cm.

Using the Pythagoras theorem in ΔADE, we have

(10)^2=(AE)^2+(8)^2(10)

100-64=(AE)^2100−64=(AE)

AE=6 cmAE=6cm

Now, areaof the shaded region is= area of rectangle ADCB-area of triangle ADE

$a = l{\times}b-\frac{1}{2}{\times}base{\times}heightA=l×b$

$A=8{\times}18-\frac{1}{2}{\times}6{\times}8A=8×18− </p><p>2$

A=144-24A=144−24

A=120cm²

The answer is 120cm²

Answer 2

GivEn:

• Length of rectangle (BC) = 8cm
• Breadth of rectangle (AB) = 18cm
• Hypotenuse in ∆ADE (DE) = 10cm

To finD:

• Area of shaded region (EBCD)

Solution:

before finding the area of shaded reason, we have to find the area of ABCD and ADE. After finding this, we will subtract the area of ADE from ABCD and then will find area of EBCD.

Finding area of ABCD :

ABCD is a rectangle so will use and formula of area of rectangle to find area of ABCD.

Formula using:

Area of rectangle = Length × Breadth

Where,

• Length = 8cm -----(Given)
• Breadth = 18cm -----(Given)

Finding:-

Now, we have a formula to find area of rectangle (ABCD). Now substitute values in formula:

Substituting value in formula:

Area of rectangle = Length × Breadth

=> Area of rectangle = 8×18

=> Area of rectangle = 144cm²

Finding area of ∆ ADE :

ADE is right angled triangle and we have to find it area.

Formula using:

• Area of right angled triangle = 1/2×(base×height)

Here, we need to find base of triangle to find area. we will use Pythagoras theorem to find it :

• Pythagoras theorem :-

Base² + Height ² = Hypotenuse²

[ Note :- This theorem is applicable only in right angled triangle. ]

Where,

• Base (AE) = ?
• Hypotenuse(DE) = 10cm ---(Given)
• Height(AD) = 8cm ---(Given)

Finding Height :

Base² + Height ² = Hypotension ²

=> Base² + 8² = 10²

=> base² + 64 = 100

=> base² = 100 - 64

=> base² = 36

=> base = √36

=> base = 6cm

Now,

We will find area of triangle by given formula = 1/2×base×height

=> Area of right angled triangle = 1/2×(base×height)

=> 1/2(6×8)

=> 1/2×48

=> 24cm²

Hence,

Area of rectangle ABCD = 144cm² and area of ∆ ADE is 24cm²

Finding area of shaded reason (EBCD) :

We will subtract the area of ∆ ADE from the area of rectangle ABCD.

=> Area of EBCD = 144cm² - 24cm²

=> Area of EBCD = 120cm²

Our answer :-

Area of shaded reason (EBCD) = 120cm²