Trapezium
A trapezium is a quadrilateral having
one pair of parallel opposite sides.
Base
Height
Base
Area of Trapezium
Parallelogram
A parallelogram is a simple quadrilateral
with two pairs of parallel sides.
Rhombus
A rhombus is a parallelogram in which
all four sides are of equal length.
The diagonals bisect each other at
right angles (90°).
Area of Rhombus
Perimeter of Rhombus
You need to know Pythagoras Theorem
Objective Type Questions
(1 Mark)
Find the area ( in cm2 ) of a trapezium whose parallel sides are 38.7 cm
and 22.3 cm, and the distance between them is 16 cm.
A. 516 B. 488 C. 396 D. 408
Correct answer: B
Analysis
The area of a rhombus (in sq.cm) of side 4cm and diagonals of length
7cm and 6cm is:
A. 16 B. 21 C. 26 D. 32
Correct answer: B
Analysis /
The area of a trapezium is 1080cm2 . If the lengths of its parallel sides
be 55 cm and 35 cm, find the distance between them.
A. 18 cm B. 20.5 cm C. 24 cm D. 19 cm
Correct answer: C
Analysis
The area of a trapezium is 405cm2 . Its parallel sides are in the ratio 4 :
5 and the distance between them is 18 cm. Find the length of each of
the parallel sides.
A. 28 cm , 35 cm
B. 12 cm , 15 cm
C. 20 cm, 25 cm
D. 24 cm , 30 cm
Correct answer: C
Analysis
The area of a trapezium is 180 cm2 and its height is 9 cm. If one of the
parallel sides is longer than the other by 6 cm, find the smaller parallel
side.
A. 17 cm B. 18 cm C. 16 cm D. 19 cm
Correct answer: A
Analysis
The area of a rhombus is 240 cm2 and one of the diagonals is 16 cm.
Find the other diagonal.
A. 18 cm B. 30 cm C. 22 cm D. 34 cm
Correct answer: B
Analysis
A school principal wants to renovate the assembly hall by tiling its
floor. The floor consists of 3000 rhombus-shaped tiles, and each tile
has diagonals of 45 cm and 30 cm. Calculate the total area of the floor.
[Passage based question]
A. 1075000cm2
B. 125000cm2
C. 2025000cm2
D. 1675000cm2
Correct answer: C
Analysis Area of 1 rhombus shaped tile = 1
× diagonal1 ×
2
diagonal2
= 12 × 45 × 30
= 675cm2
Area of 3000 tiles = 3000 × 675 = 2025000cm2
Problem Solving - Difficult
The parallel sides of a trapezium are 25 cm and 13 cm; its
nonparallel sides are equal, each being 10 cm. Find the
area of the trapezium.
13 cm
D C
cm
10
cm
10
A B
M L
25 cm
Construction
13 cm
cm D C
10
cm
10
13 cm
A B
M L
The parallel sides of a trapezium are 25 cm and 13 cm; its nonparallel
sides are equal, each being 10 cm. Find the area of the trapezium.
A. 196cm2 B. 136cm2 C. 182cm2 D. 152cm2
Correct answer: D
Analysis
The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel
sides are both equal, each being 13 cm. Find the area of the trapezium.
A. 194cm2
B. 116cm2
C. 180cm2
D. 145cm2
Correct answer: C
Analysis
Problem Solving - Difficult
12
9
6 8 4
Area of triangle ANE =
Area of triangle DMC =
12
9
6 8 4
Area of trapezium DENM =
Area of trapezium ABC =
In the given figure, is a quadrilateral in which AC =24 cm, BL ⊥ AC and
DM ⊥ AC such that BL = 8 cm and DM =7 cm. Find the area of quad.
ABCD.
A. 120 cm² B. 180 cm² C. 130 cm² D. 150 cm²
Correct answer: B
Analysis
Find the area of given figure ABCDEFGH as per dimensions given in it.
A. 38 cm² B. 53 cm² C. 68 cm² D. 43 cm²
Correct answer: C
Analysis
Find the area of a regular hexagon ABCDEF in which each side
measures 13 cm and whose height is 23 cm, as shown in the given
figure.
A. 532 cm² B. 232 cm² C. 432 cm² D. 332 cm²
Correct answer: C
Analysis
A wall decoration is in the shape given below. Decoration is made of
four congruent mirrors. The sides of a mirror are of the same length. [
CBSE - SAS]
(a) What is the area occupied by the decoration on the wall?
A. 96 cm2 B. 84 cm2 C. 128 cm2 D. 100 cm2
Correct answer: D
Analysis
A wall decoration is in the shape given below. Decoration is made of
four congruent mirrors. The sides of a mirror are of the same length. [
CBSE - SAS]
(b) Rohan pasted four more mirrors congruent to the earlier ones.
What is the area of the new wall decoration?
A. 180 cm2 B. 200 cm2 C. 168cm2 D. 175 cm2
Correct answer: B
Analysis
