Areas of Parallelograms and Triangles Test

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Areas of Parallelograms and Triangles Test - 1

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Weekly Quiz Competition

Question 1
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The median of a triangle divides it into two

A
right angles.

B
congruent triangles.

C
triangles of different areas.

D
isosceles triangles.

Solution

Explanation:

The median of a triangle divides it into two triangles of different areas.

If in a triangle ABC, AD is a median, then

Area of triangle ABD = Area of triangle ACD.
Question 2
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The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 16 cm and 12 cm is

A
48 cm².

B
28 cm².

C
24 cm².

D
96 cm².

Solution

Explanation:

Since the figure obtained by joining the mid-points of the adjacent sides of a rhombus is rectangle, then

Side of rectange = PQ = 1/2AC

[Mid-point theorem]

=> PQ = 1/2 x 16 = 8 cm

Similarly, QR = 1/2 x 12 = 6 cm

Therefore, Area of rectangle PQRS = PQ x QR = 8 x 6 = 48 cm²

The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 16 cm and 12 cm is a rectangle with are 48 sq. cm.
Question 3
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The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is

A
a square of area 26 cm².

B
a rectangle of area 24cm²

C
a rhombus of area 24cm².

D
a trapezium of area 14cm².

Solution

Explanation:

Since figure obtained by joining the mid-points of the adjacent sides of a rectange is a rhombus.

Then diagonals of the rhombus PQRS are QS and PR i.e., sides of rectangle ABCD.

Therefore, QS = 8 cm and PR = 6 cm

Now, Area of rhombus PQRS = 1/2x QS x PR = 1/2x 8 x 6 = 24 cm²

The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is a rhombus with area 24 sq. cm.
Question 4
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ABCD is quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD

A
is a parallelogram

B
is a rhombus

C
is a rectangles

D
need not be any of (a), (b) or (c).

Solution

Explanation:

ABCD is quadrilateral whose diagonal AC divides it into two parts, equal in area, then ABCD can be either a rhombus or a rectangle or a parallelogram.

Therefore, it needs not be any of (a), (b) or (c).
Question 5
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Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is

A
it is 1 : 2.

B
it is 3 : 1.

C
it is 2 : 1.

D
it is 1 : 1.

Solution

Explanation:

Two parallelograms are on equal bases and between the same parallels. The ratio of their areas is 1 : 1.

Becasue when two parallelogram are on same base and between the same parallels, then the areas of both parallelograms are equal.
Question 6
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The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to

A
1/2 ar (△ABC).

B
1/4 ar (△ABC).

C
ar (△ABC).

D
1/3 ar (△ABC).

Solution

Explanation:

Mid-point theorem says that the mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to

1/2 × area (ΔABC).
Question 7
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If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio of the area of the triangle to the area of the parallelogram is

A
it is 1 : 2.

B
it is 1 : 4.

C
it is 3 : 1.

D
it is 1 : 4.

Solution

Explanation:

If a triangle and a parallelogram are on the same base and between the same parallels, then the ratio of the area of the triangle to the area of the parallelogram is 1 : 2.

Area of triangle = 1/2x Area of parallelogram

=>Area of triangle : Area of parallelogram = 1 : 2

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Re-Attempt Weekly Quiz Competition

Areas of Parallelograms and Triangles Test - 1

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Areas of Parallelograms and Triangles Test - 1

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Question 1

right angles.

congruent triangles.

triangles of different areas.

isosceles triangles.

Solution

Question 2

48 cm2.

28 cm2.

24 cm2.

96 cm2.

Solution

Question 3

a square of area 26 cm2.

a rectangle of area 24cm2

a rhombus of area 24cm2.

a trapezium of area 14cm2.

Solution

Question 4

is a parallelogram

is a rhombus

is a rectangles

need not be any of (a), (b) or (c).

Solution

Question 5

it is 1 : 2.

it is 3 : 1.

it is 2 : 1.

it is 1 : 1.

Solution

Question 6

1/2 ar (△ABC).

1/4 ar (△ABC).

ar (△ABC).

1/3 ar (△ABC).

Solution

Question 7

it is 1 : 2.

it is 1 : 4.

it is 3 : 1.

it is 1 : 4.

Solution

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48 cm².

28 cm².

24 cm².

96 cm².

a square of area 26 cm².

a rectangle of area 24cm²

a rhombus of area 24cm².

a trapezium of area 14cm².