3 Mark Question

Question 13 Marks

Length of the two parallel sides of a trapezium are 8.5 cm and 11.5 cm respectively and its height is 4.2 cm, find its area.

Answer

Length of the two parallel sides of a trapezium are $8.5 cm$ and $11.5 cm$ and its height is $4.2 cm$.
Area of a trapezium
$=\frac{1}{2} x$ sum of lengths of parallel sides $\times$ height
$=\frac{1}{2} \times(8.5+11.5) \times 4.2$
$=\frac{1}{2} \times 20 \times 4.2$
$=10 \times 4.2$
$=42 sq \cdot cm$
$\therefore$ The area of the trapezium is 42 sq. cm.

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Question 23 Marks

In the given figure, ☐ABCD is a trapezium, side AB || side DC, l(AB) = 13 cm, l(DC) = 9 cm, l(AD) = 8 cm, find the area ☐ABCD.

Answer

$\square A B C D$ is a trapezium, side $A B \|$ side $D C$, $I(A B)=13 cm , I(D C)=9 cm , l(A D)=8 cm$
Area of a trapezium $=\frac{1}{2} x$ sum of lengths of parallel sides $x$ height
$
\begin{aligned}
& \therefore A(\square A B C D)=\frac{1}{2} \times[I(A B)+I(D C)] \times I(A D) \\
& =\frac{1}{2} \times(13+9) \times 8 \\
& =\frac{1}{2} \times 22 \times 8 \\
& =11 \times 8 \\
& =88 \text { sq.cm }
\end{aligned}
$
$\therefore$ The area of $\square ABCD$ is $88 sq . cm$.
[Note: The question is modified.]

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Question 33 Marks

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 $\times$ height
$
\begin{aligned}
& \therefore 83.2=\text { base } \times 6.4 \\
& \therefore \text { base }=\frac{83.2}{6.4}=13 cm
\end{aligned}
$
$\therefore$ The length of the base of the parallelogram is $13 cm$.

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Question 43 Marks

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 $\times$ height
$\therefore 29.6=8 \times$ height
$\therefore$ height $=\frac{29.6}{8}=3.7 cm$
$\therefore$ Height of the parallelogram is $3.7 cm$.

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Question 53 Marks

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 × 11
= 198 sq.cm
∴ Area of the parallelogram is 198 sq.cm.

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Question 63 Marks

Draw a big enough parallelogram ABCD on a paper as shown in the figure.
Draw perpendicular AE on side BC.
Cut the right angled ∆AEB. 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.
∴ Area of a parallelogram = base × height

Answer

Draw a big enough parallelogram ABCD on a paper as shown in the figure.
Draw perpendicular AE on side BC.
Cut the right angled ∆AEB. 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.
∴ Area of a parallelogram = Area of a rectangle = length × breadth = base × height

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