RD Chapter 15- Areas of Parallelograms and Triangles Ex-15.1 |
RD Chapter 15- Areas of Parallelograms and Triangles Ex-15.3 |
RD Chapter 15- Areas of Parallelograms and Triangles Ex-VSAQS |

**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

**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

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

**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

If ABCD is a parallelogram, then prove that

ar (ΔABD) = ar (ΔBCD) = ar (ΔABC) = ar (ΔACD) = 1212 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)

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