The RS Aggarwal Solutions for Class 7 Maths Exercise 20C Chapter 20 Mensuration, contains different questions with various solutions to the problems. This exercise of RS Aggarwal Solutions for Class 7 Chapter 20 includes questions related to the area of a parallelogram and the area of rhombus. Students have to practice RS Aggarwal Solutions for Class 7 Chapter 20 regularly and become an expert in the Maths. To strengthen the fundamentals and be able to solve RS Aggarwal Solutions for Class 7 Maths Chapter 20 Mensuration questions that are usually asked in the final exam.

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**1. Find the area of a parallelogram with base 32 cm and height 16.5 cm.**

**Solution:-**

From the question is given that,

Base of the parallelogram = 32 cm

Height of the parallelogram = 16.5 cm

âˆ´area of the parallelogram = base Ã— height

= 32 Ã— 16.5

= 528 cm^{2}

**2. The base of a parallelogram measures 1 m 60 cm and its height is 75 cm. Find its area in m ^{2}.**

**Solution:-**

From the question is given that,

Base of the parallelogram = 1 m 60 cm

= 1 m + (60/100) m [Because 1 m = 100 cm]

= 1 + 0.6

= 1.6 m

Height of the parallelogram = 75 cm

= 75/100 [Because 1 m = 100 cm]

= 0.75 m

âˆ´area of the parallelogram = base Ã— height

= 1.6 Ã— 0.75

= 1.2 m^{2}

**3. In a parallelogram it is being given that base = 14 dm and height = 6.5 dm. Find its area in (i) cm ^{2} **

**(ii) m ^{2}.**

**Solution:-**

(i) Area in cm^{2}

From the question is given that,

Base of the parallelogram = 14 dm

= 14 Ã— 10 [Because 1 dm = 10 cm]

= 140 cm

Height of the parallelogram = 6.5 dm

= 6.5 Ã— 10 [Because 1 dm = 10 cm]

= 65 cm

âˆ´area of the parallelogram = base Ã— height

= 140 Ã— 65

= 9100 cm^{2}

(i) Area in m^{2}

From the question is given that,

Base of the parallelogram = 14 dm

= 14/10 [Because 1 m = 10 dm]

= 1.4 m

Height of the parallelogram = 6.5 dm

= 6.5/10 [Because 1 m = 10 dm]

= 0.65 m

âˆ´area of the parallelogram = base Ã— height

= 1.4 Ã— 0.65

= 0.91 m^{2}

**4. Find the height of a parallelogram whose area is 54 cm ^{2} and the base is 15 cm.**

**Solution:-**

From the question is given that,

Base of the parallelogram = 15 cm

Area of the parallelogram = 54 cm^{2}

âˆ´area of the parallelogram = base Ã— height

54 = 15 Ã— height

Height = 54/15

Height = 3.6 cm

Hence, the height of the parallelogram is 3.6 cm

**5. One side of a parallelogram is 18 cm long and its area is 153 cm ^{2}. Find the distance of the given side from its opposite side.**

**Solution:-**

From the question is given that,

Base of the parallelogram = 18 cm

Area of the parallelogram = 153 cm^{2}

âˆ´area of the parallelogram = base Ã— height

153 = 18 Ã— height

Height = 153/18

Height = 8.5 cm

Hence, the distance of the given side from its opposite side is 8.5 cm

**6. In a parallelogram ABCD, AB = 18 cm, BC = 12 cm, AL âŠ¥ DC and AM âŠ¥ BC.**

**If AL = 6.4 cm, find the length of AM.**

**Solution:-**

From the question is given that,

Base of parallelogram, AB = 18 cm

Height of the parallelogram, AL = 6.4 cm

Then,

Area of the parallelogram ABCD = base Ã— height

= 18 Ã— 6.4

= 115.2 cm^{2} â€¦ [eqn. 1]

Now, let us take BC as the base of parallelogram ABCD,

Then,

Area of the parallelogram ABCD = base Ã— height

= 12 Ã— MA

= 12MA cm^{2} â€¦ [eqn. 2]

From the equation (1) and (2)

= 12MA = 115.2 cm^{2}

= MA = (115.2/12)

= MA = 9.6 cm

Hence, the length of AM is 9.6 cm

**7. The adjacent sides of a parallelogram are 15 cm and 8 cm. If the distance between the longer sides is 4 cm, find the distance between the shorter sides.**

**Solution:-**

Let us assume ABCD is a parallelogram with side AB of length 15 cm and the corresponding altitude AE of length 4 cm.

The adjacent side AD is of length 8 cm and the corresponding altitude is CF.

WKT, Area of parallelogram = Base Ã— height

Thus, we have two altitudes and two corresponding bases.

âˆ´AD Ã— CF = AB Ã— AE

= 8 cm Ã— CF = 15 cm Ã— 4 cm

= CF = (15 Ã— 4)/8

= CF = (15/2)

= CF = 7.5 cm

âˆ´The distance between the shorter side 7.5 cm

**8. The height of a parallelogram is one-third of its base. If the area of the parallelogram is 108 cm ^{2}, find its base and height.**

**Solution:-**

Let us assume the base of the parallelogram be x cm.

and height of the parallelogram will be (1/3)x cm.

From the question it is given that the area of the parallelogram is 108 cm^{2}.

âˆ´Area of the parallelogram = base Ã— height

= 108 = (x) Ã— ((1/3)x)

= 108 = (1/3)x^{2}

= x^{2} = (108 Ã— 3)

= x^{2} = 324

= x = âˆš324

= x = 18

Then,

The base of the parallelogram be x is 18 cm

Height of the parallelogram will be (1/3)x = (1/3) Ã— 18 = 6 cm