Areas of Parallelograms and Triangles Test

Result

Areas of Parallelograms and Triangles Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

If two triangles are on the same base and between the same parallels then the ratio of their areas is

A
1 : 2

B
1 : 3

C
2 : 3

D
1 : 1

Solution

Area of triangle = half of base x height
Given they have same base.
They lie between same parallel line means they have same height that is distance between parallel lines.
So they have same area
So correct answer should be Option D
Question 2
1 / -0

ABCD is a rectangle, ABEF is a parallelogram with area of $$30 \ cm^2$$ and AB and CF are parallel. Find area of rectangle ABCD

A
$$30\ sq\ units$$

B
$$40\ sq\ units$$

C
$$50\ sq\ units$$

D
$$60\ sq\ units$$

Solution

Given ABCD is a rectangle ABEF is a parallelogram
area of $$ABEF = 30cm^2$$
base $$\times$$ height $$= 30cm^2$$
$$AB \times CB = 30cm^2$$
In rectangle $$ABCD(AD = BC)$$
area $$= AB \times CB = 30cm^2$$
Length $$\times$$ breadth $$=30cm^2$$
area of rectangle $$=30cm^2$$
Option A is correct
Question 3
1 / -0

In the given figure, area of the parallelogram $$ABCD$$ is $$48$$ $$cm^2$$ and $$FC \parallel AB$$. Find the area of the parallelogram $$ABEF$$.

A
$$12\ cm^2$$

B
$$24\ cm^2$$

C
$$48\ cm^2$$

D
$$8\ cm^2$$

Solution

$$\Rightarrow$$ In given figure, we can see that parallelogram $$ABCD$$ and parallelogram $$ABEF$$ both are lies between same parallel line that is $$FC$$ and $$AB$$.
$$\Rightarrow$$ And parallelogram $$ABCD$$ and $$ABEF$$ contains same base that is $$AB$$.
$$\Rightarrow$$ So, we know that parallelogram on same base and between same parallels are equal in area.
$$\Rightarrow$$ So, $$Area(ABCD)=Area(ABEF)$$ ------ ( 1 )
$$\Rightarrow$$ We have given $$Area(ABCD)=48\ cm^2$$
From $$( 1 )$$ we get,
Area of parallelogram $$ABEF=48\ cm^2$$
Question 4
1 / -0

For figures on same base and same parallels, the figures have to lie between same _______

A
parallels

B
bases

C
heights

D
none of these

Solution
Question 5
1 / -0

For figures on same base and same parallels, the figures have to lie between same parallels

A
Yes

B
no

C
Only in exceptional cases

D
None of these

Solution
Question 6
1 / -0

On the basis of given figure, we can conclude that

A
triangle $$DCF$$ and parallelogram $$ABCD$$ lies on same base

B
triangle $$DCF$$ and quadrilateral $$AECB$$ lies on same base

C
triangle $$ADE$$ and parallelogram $$ABCD$$ lies on same base

D
None of these
Question 7
1 / -0

Name the common base on which both the figures, $$\triangle ABF$$ and parallelogram $$ABCD$$ lies (if any), on the basis of given diagram.

A
$$CD$$

B
$$AB$$

C
$$AD$$

D
$$BC$$

Solution
Question 8
1 / -0

In given diagram, there are two different parallelograms with same base $$AB$$ and both are between same parallel lines. If the $$AB = 6$$ $$cm$$ and height of the parallelogram $$ABCD$$ is $$5$$ $$cm$$, then what will be the area of parallelogram $$ABEF$$

A
$$25$$ $$cm^2$$

B
$$30$$ $$cm^2$$

C
$$36$$ $$cm^2$$

D
None of these

Solution

We first begin by observing that ABCD and ABEF lie on the same base AB and between the same parallels.
$$\therefore$$ $$Ar(ABCD) = Ar(ABEF)$$

$$Ar(ABCD) = 6\times 5 = 30cm^2 = Ar(ABEF)$$
Question 9
1 / -0

Area of any two parallelograms ia equal if they have common ____ and both are between same parallels.

A
diagonals

B
sides

C
base

D
none of these

Solution
Question 10
1 / -0

In which of the following figures, you find two polygons on the same base and between the same parallels?

A

B

C

D
None of these

Solution