Areas Of Triangles And Parallelograms(9th Grade > Mathematics ) Questions and answers for exam Preparation

9th Grade > Mathematics

AREAS OF TRIANGLES AND PARALLELOGRAMS MCQs

Total Questions : 51 | Page 1 of 6 pages

Question 1. If 1, 2, 3 and 4 represent the areas of the four triangles (of a parallelogram) with different shades, then _______.

2 = 3, 1 ≠ 4
1 = 2 = 3 = 4
1 ≠ 2, 3 = 4
1 = 2, 3 ≠ 4

Discuss Question

Answer: Option B. -> 1 = 2 = 3 = 4
:
B
Consider the figure below:

△ D A O and △ O C B

∠ D A O = ∠ O C B (Alternate angles) ∠ A D O = ∠ C B O (Alternate angles) A D = C B (Opposite sides of parallelogram) Hence, Δ A D O ≅ Δ C B O (AAS congruence) Similarly it can be proved that A r e a (Δ D O C) = A r e a (Δ (B O A)

△ A B D

, AO is the median.
A median divides a triangle into two equal parts.
Hence 1 = 4
Similarly 2 = 3

∴ 1 = 2 = 3 = 4

Question 2. In parallelogram ABCD shown below, the vertical distance between the lines AD and BC is 5 cm and length of BC is 4 cm. P and Q are the midpoints of AB and AD respectively. Area of triangle AQP is ____.

1.25 cm2
2.5 cm2
5 cm2
Insufficient data

Discuss Question

Answer: Option B. -> 2.5 cm2
:
B

Given:
ABCD is a parallelogram.
Base BC = 4 cm
Height of a parallelogram = 5 cm
Area of parallelogram ABCD = Base xHeight

= 5 c m \times 4 c m

= 20 c m^{2}

A diagonal divides a parallelogram in two congruent triangles which have equal areas.

∴ A r e a Δ A B D = A r e a Δ B D C

∴ A r e a Δ A B D

\frac{1}{2}

Area of ABCD

= 10 c m^{2}

Let R be the midpoint of the diagonal. Join P and Q to R.
P and Q are midpoints of AB and AD.
Therefore PQ is parallel to BD (Midpoint theorem)
Similarly, QR is parallel to AB and PR is parallel to AD
Therefore, APQR, DQPR and BPQR are all parallelograms

∴ A r e a Δ A Q P = A r e a Δ R Q P

= A r e a Δ B P R = A r e a Δ Q P R

...(i)

A r e a Δ A B D = A r e a Δ A Q P + A r e a Δ R Q P + A r e a Δ B P R + A r e a Δ Q P R

A r e a Δ A B D = 4 \times A r e a Δ A Q P

= \frac{1}{4} \times A r e a Δ A B D

∴ A r e a Δ A Q P = \frac{1}{4} \times 10

= 2.5 c m^{2}

Question 3. A parallelogram and a triangle are on equal base and between the same parallel lines. The ratio of their areas is ______.

Discuss Question

Answer: Option A. -> 2:1
:
A
Consider the figure given below.

A Parallelogram And A Triangle Are On Equal Base And Between...

In this figure, ABCD is a parallelogram and ABE is a triangle. Both of them have the same base i.e., AB. The perpendicular EF is an altitude for both triangle and parallelogram.
Now area of

Δ A B E = \frac{1}{2} A B \times E F

And area of parallelogram is

A B \times E F

.
Hence, Area of parallelogram is twice that of triangle and the ratio will be 2:1

Question 4. In the adjoining figure,

Δ Q P R

is right-angled at Q in which QR = 6 cm and PQ = 7 cm. Find the area of

Δ Q S R

, given that PS is parallel to QR.

In The Adjoining Figure, ΔQPR Is Right-angled At Q In Which...

21 cm2
20 cm2
10 cm2
11 cm2

Discuss Question

Answer: Option A. -> 21 cm2
:
A

Area of right angled triangle PQR
=

\frac{1}{2}

x Base x Height
=

\frac{1}{2}

x QR x PQ
=

\frac{1}{2}

x 6 x 7

= 21 c m^{2}

Δ Q P R

and

Δ Q S R

lie on same base QR and are between same parallels hence, their areas are equal.
Area

Δ Q P R

= Area

Δ Q S R

∴ A r e a o f Δ Q S R = 21 c m^{2}

Question 5.

ABCD is a trapezium in which AB || DC. Diagonals AC and BD intersect each other at O. Find the triangle which is equal to the area of

△

BOC.

ΔADC
ΔAOB
ΔDOC
ΔAOD

Discuss Question

Answer: Option D. -> ΔAOD
:
D

It can be observed that ΔDAC and ΔDBC lie on the same base DC and between the same parallels AB and CD.
∴ Area (ΔDAC) = Area (ΔDBC)
SubtractingArea (ΔDOC) on both the sides
⇒ Area (ΔDAC) − Area (ΔDOC) = Area (ΔDBC) − Area (ΔDOC)
⇒ Area (ΔAOD) = Area (ΔBOC)

Question 6. The part of the plane enclosed by a simple closed figure is called a ___ region.

Discuss Question

:
The part of the plane enclosed by a simple closed figure is called a planar region. The magnitude or measure of this planar region is called its area.

Question 7. ABCD is a parallelogram whose area is 54

c m^{2}

. The area of triangle AEB is __

c m^{2}

ABCD Is A Parallelogram Whose Area Is 54 Cm2. The Area Of ...

Discuss Question

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

Thus, area of triangle AEB is \frac{1}{2} \times 54 = 27 c m^{2}

Question 8. What is the area of

△ A B C

(in square cm) if AD is the median and area

△ A D B

= 18 square cm?

What Is The Area Of △ABC (in Square Cm) If AD Is The Media...

Discuss Question

A median of the triangle divides it into two triangles of equal area.
So, Area (

△ A B C

) = 2 × Area (

△ A D B

) = 2 × 18 = 36 square cm.

Question 9. In the rectangle ABCD, O is any point inside the rectangle. If area( ΔAOD) = 30

c m^{2}

and area( ΔBOC) = 60

c m^{2}

, area of the rectangle ABCD is
___
(in

c m^{2}

)

In The Rectangle ABCD, O Is Any Point Inside The Rectangle. ...

Discuss Question

Draw a line through O parallel to A D as shown. Parallelogram A P Q D and triangle A O D are on same base A D and between same parallels. So, Area (A O D) = \frac{1}{2} Area (A P Q D) Area (A P Q D) = 60 c m^{2} Parallelogram P B C Q and triangle B O C are on same base BC and between same parallels. So, Area (B O C) = \frac{1}{2} Area (P B C Q) Area (P B C Q) = 120 c m^{2} Area (A B C D) = Area (A P Q D) + Area (P B C Q) = 180 c m^{2}

Question 10. ABC is a triangle in which D, E, F are the mid-points of BC, AC and AB respectively. If Area (ΔABC) = 32 cm², then area of trapezium BFEC is ______