Question

Easy question :)

In the given figure, BD is a diagonal of quadrilateral ABCD. Find the area of ABCD. (Figure in the attachment).

Options :

a) 35 cm²
b) 35/2 cm²
c) 70 cm²
d) 140 cm²

Explanation needed :)

Thanks! ​

Answer 1

Hi Aanya ! Here is your Answer !

Given :

• Hight of the quadrilateral = 7 cm
• AB = 5cm
• CD = 5cm

To Find :

• Area of the quadrilateral ABCD ?

Formula To Be Used !

We will use the formula of area of Parallelogram

• Area = base×hieght

We will also use the formula of area of right triangle

• Area = ½×Hieght×base

Process :

• As Given in the question, the quadrilateral ABCD is divided into 2 right triangle.
• As we can clearly see that the two opposite side of the quadrilateral are equal.
• Also, The angles are 90° Hence, equal
• Means ABCD is a parallelogram.
• hence we can find out its area by using the Formula of area of parallelogram

• But, for your convenience Also, I will split the quadrilateral in two triangles as Given and fund area of each

Solution :

Method 1 :

If we prove that ABCD is a parallelogram, then we can use the formula of area I parallelogram to find the area.

As we have already proved in the 'Process' section, we will proceed further.

As Given, Hieght = 7cm

Corresponding base = 5cm

$\tt{Area \: _{Parallelogram} = base \times height}$

$\implies \tt{Area_{Parallelogram} = 5 \times 7}$

$\red{ \underline{ \boxed{ {\tt{ \implies Area_{Parallelogram} = 35 {cm}^{2} }}}}}$

Hence, Area of the parallelogram = 35cm²

Hence, Option A) is correct

__________________________

Method 2 :

We will find the area of parallelogram using the area of both triangle

Let triangle ABD = triangle1

Let triangle BDC = Triangle2

Area of triangle = ½×b×h

Hence, we get that:

$\tt{ \implies Area_{Parallelogram} = area_{triangle_1} + area_{triangle_2}}$

$\tt{ \implies area_{parallelogram} = ( \frac{1}{2} \times 5 \times 7) + ( \frac{1}{2} \times 5 \times 7)}$

$\tt{ \implies \: area_{parallelogram} = 2( \frac{1}{2} \times 5 \times 7)}$

$\tt{ \implies area_{parallelogram} = 2 \times \frac{1}{2} \times 5 \times 7}$

$\implies \tt{area_{parallelogram} = 5 \times 7}$

$\blue{ \underline{ \boxed{ \tt{ \implies area_{parallelogram} = 35 {cm}^{2} }}}}$

Hence, Area of parallelogram = 35cm²

Hence, Option A) is correct