RD Sharma 2020 solution class 9 chapter 14 Area of Parallelograms and Triangles Exercise 14.2

Exercise 14.2

Page-14.15

Question 1:

If the given figure, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm. AE = 8 cm and CF = 10 cm, find AD.
 

Answer 1:

Given: Here in the question it is given

(1) ABCD is a parallelogram,

(2) and

(3) , AB = 16 cm

(4) AE = 8cm

(5) CF = 10cm

To Find : AD =?

Calculation: We know that formula for calculating the

Therefore,

Area of paralleogram ABCD = DC × AE (Taking base as DC and Height as AE )

Area of paralleogram ABCD = AB × AE (AB = DC as opposite side of the parallelogram are equal)

Therefore,

Area of paralleogram ABCD = 16 × 8 ……(1)

Taking the base of Parallelogram ABCD as AD we get

Area of paralleogram ABCD = AD × CF (taking base as AD and height as CF)

Area of paralleogram ABCD = AD × 10 ……(2)

Since equation 1 and 2 both represent the Area of the same Parallelogram ABCD , both should be equal.

Hence fro equation (1) and (2),

This means that,

Hence we get the result as

Question 2:

In Q.No. 1, if AD = 6 cm, CF = 10 cm, and AE = 8 cm, find AB.

Answer 2:

Given: Here in the question it is given that

(1) ABCD is a parallelogram,

(2) and

(3)

(4) AD = 6 cm

(5) AE = 8cm

(6) CF = 10cm

To Find : AB =?

Calculation: We know that formula for calculating the

_{Area of paralleogram = base × height}

Therefore,

Area of paralleogram ABCD = DC × AE (Taking base as DC and Height as AE )

Area of paralleogram ABCD = AB × AE (AB = DC as opposite side of the parallelogram are equal)

Therefore, Area of paralleogram ABCd = 16 × 8

Area of Parallelogram ABCD = AB× 8 ……(1)

Taking the base of Parallelogram ABCD as AD we get

Area of paralleogram ABCD = AD × CF (taking base as AD and height as CF)

Area of paralleogram ABCD = 6 × 10 ……(2)

Since equation 1and 2 both represent the Area of the same Parallelogram ABCD , both should be equal.

Hence equation 1 is equal to equation 2

Which means that,

Hence we got the measure of AB equal to

 

Question 3:

Let ABCD be a parallelogram of area 124 cm². If E and F are the mid-points of sides AB and CD respectively, then find the area of parallelogram AEFD.

Answer 3:

Given: Here in the question it is given that

(1) Area of paralleogram ABCD = 124 cm²

(2) E is the midpoint of AB, which means

(3) F is the midpoint of CD, which means

To Find : Area of Parallelogram AEFD

Calculation: We know that formula for calculating the

Area of Parallelogram = base × height

Therefore,

Area of paralleogram ABCD = AB × AD (Taking base as AB and Height as AD ) ……(1)

Therefore,

Area of paralleogram AEFD = AE × AD (Taking base as AB and Height as AD ) ……(2)

()

= Area of Parallelogram ABCD (from equation1)

Hence we got the result Area of Parallelogram AEFD

 

Question 4:

If ABCD is a parallelogram, then prove that

ar (ΔABD) = ar (ΔBCD) = ar (ΔABC) = ar (ΔACD) = $\frac{1}{2}$ ar (||^gm ABCD)

Answer 4:

Given: Here in the question it is given that

(1) ABCD is a Parallelogram

To Prove :

(1)

(2)

(3)

(4)

Construction: Draw

Calculation: We know that formula for calculating the

Area of Parallelogram = base × height

Area of paralleogram ABCD = BC × AE (Taking base as BC and Height as AE ……(1)

We know that formula for calculating the

Area of ΔADC = Base × Height

(AD is the base of ΔADC and AE is the height of ΔADC)

= Area of Parallelogram ABCD (from equation1)

Hence we get the result

Similarly we can show that 

(2)

(3)

(4)