Maharashtra Board Class 8 Maths Chapter 15 Area Set 15.1 Solutions

Question 1. If base of a parallelogram is 18 cm and its height is 11 cm, find its area.
Answer: Given, base = 18 cm, height = 11 cm
Area of a parallelogram = base × height
= 18 x 11
= 198 sq.cm
Therefore, Area of the parallelogram is 198 sq.cm.
In simple words: To find the area of a parallelogram, multiply its base by its height. Here, 18 cm (base) multiplied by 11 cm (height) gives 198 sq.cm.

🎯 Exam Tip: Remember the formula for the area of a parallelogram (base × height) and ensure correct units in your final answer.

Question 2. If area of a parallelogram is 29.6 sq. cm and its base is 8 cm, find its height.
Answer: Given, area of a parallelogram = 29.6 sq.cm,
base = 8 cm
Area of a parallelogram = base × height
Therefore, 29.6 = 8 × height
Therefore, height = \( \frac{29.6}{8} \) = 3.7 cm
Therefore, Height of the parallelogram is 3.7 cm.
In simple words: Given the area and base of a parallelogram, you can find the height by dividing the area by the base. In this case, 29.6 sq.cm divided by 8 cm gives a height of 3.7 cm.

🎯 Exam Tip: When solving for a missing dimension, rearrange the area formula (Area = base × height) to isolate the unknown variable. Pay attention to decimal calculations.

Question 3. Area of a parallelogram is 83.2 sq.cm. If its height is 6.4 cm, find the length of its base.
Answer: Given, area of a parallelogram = 83.2 sq.cm, height = 6.4 cm
Area of a parallelogram = base × height
Therefore, 83.2 = base × 6.4
Therefore, base = \( \frac{83.2}{6.4} \) = 13 cm
Therefore, The length of the base of the parallelogram is 13 cm.
In simple words: To find the base of a parallelogram when the area and height are known, divide the area by the height. Here, 83.2 sq.cm divided by 6.4 cm results in a base length of 13 cm.

🎯 Exam Tip: Practice dividing decimals accurately. Always double-check that your calculated dimension makes sense in the context of the given area and other dimension.

Maharashtra Board Class 8 Maths Chapter 15 Area Practice Set 15.1 Intext Questions And Activities

Question 1. Draw a big enough parallelogram ABCD on a paper as shown in the figure.
Draw perpendicular AE on side BC.
Cut the right angled ΔΑΕΒ. Join it with the remaining part of ABCD as shown in the figure.
The new figure formed is a rectangle.
The rectangle is formed from the parallelogram.
So, areas of both the figures are equal.
Base of parallelogram is one side (length) of the rectangle and its height is the other side (breadth) of the rectangle.
Solution:
ℹ️ चित्र व्याख्या (Diagram Explanation): पहले चित्र में एक समांतर चतुर्भुज ABCD दिखाया गया है, जिसमें बिंदु A से भुजा BC पर एक लंब AE खींचा गया है। दूसरा चित्र दर्शाता है कि समकोण त्रिभुज ΔAEB को काटकर समांतर चतुर्भुज के शेष भाग के साथ इस प्रकार जोड़ा गया है कि वह एक आयत का रूप ले लेता है, जिससे यह सिद्ध होता है कि समांतर चतुर्भुज का क्षेत्रफल उसके आधार और ऊँचाई के गुणनफल के बराबर होता है।
Draw a big enough parallelogram ABCD on a paper as shown in the figure.
Draw perpendicular AE on side BC.
Cut the right angled ΔΑΕΒ. Join it with the remaining part of ABCD as shown in the figure.
The new figure formed is a rectangle.
The rectangle is formed from the parallelogram.
So, areas of both the figures are equal.
Base of parallelogram is one side (length) of the rectangle and its height is the other side (breadth) of the rectangle.
Therefore, Area of a parallelogram = Area of a rectangle = length × breadth = base × height
In simple words: This activity visually demonstrates that a parallelogram can be transformed into a rectangle by cutting a right-angled triangle from one end and attaching it to the other. Since the dimensions of the rectangle correspond to the base and height of the parallelogram, their areas are equal, thus proving the formula for the area of a parallelogram.

🎯 Exam Tip: Understanding this visual proof helps solidify the concept of the area of a parallelogram. Be able to explain how the transformation leads to the area formula.