18. Area of a Trapezium and a Polygon
Exercise 18A
1. Question
Find the area of a trapezium whose parallel sides are 24 cm and 20 cm and the distance between them is 15
cm.
Answer
Given:
Length of parallel sides is 24cm and 20 cm
Height (h) = 15 cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore, Area of trapezium = × (24 +20) × 15 =330 cm2.
2. Question
Find the area of a trapezium whose parallel sides are 38.7 cm and 22.3 cm, and the distance between them
is 16 cm.
Answer
Given
Length of parallel sides is 38.7cm and 22.3 cm
Height (h) = 16 cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium = × (38.7 +22.3) × 16 = 488 cm2.
3. Question
The shape of the top surface of a table is trapezium. Its parallel sides are 1 m and 1.4 m and the
perpendicular distance between them is 0.9 cm. Find its area.
Answer
Given
Length of parallel sides is 1m and 1.4m
Height (h) = 0.9m
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium = × (1 +1.4) × 0.9
=1.08 m 2.
4. Question
The area of a trapezium is 1080 cm2. If the lengths of its parallel sides be 55 cm and 35 cm, find the distance
,between them.
Answer
Given
Length of parallel sides is 55cm and 35 cm
Area of trapezium= 1080 cm2
Let Height (h) =y cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium is × (55 + 35) × y =1080 cm2.
× (90) × y =1080
⇒ 45 × y =1080
⇒y= = 24
... Distance between the parallel lines is 24 cm.
5. Question
A field is in the form of a trapezium. Its area is 1586 m 2 and the distance between its parallel sides is 26 m. If
one of the parallel sides is 84 m, find the other.
Answer
Given
Let length of parallel sides be 84cm and y cm
Area of trapezium= 1586 cm2
Let Height (h) =26 cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium is × (84 +y) × 26 =1586 cm2.
× (84 +y) × 26 =1586
⇒(84 + y) × 13 =1586
⇒ 84 + y =
⇒ y =122— 84 = 38
... Length of the other parallel side is 38 cm.
6. Question
The area of a trapezium is 405 cm2. Its parallel sides are in the ration 4:5 and the distance between them is
18 cm. Find the length of each of the parallel sides.
Answer
Given
Lengths of the parallel sides are in the ratio 4:5
Therefore let one of the side length be 4X and other side length be 5X
, Area of trapezium= 405 cm2
Let Height (h) =18 cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium is x (4X +5X) × 18 =405 cm2.
× (4X + 5X) × 18 =405
⇒(9X) × 9 =405
⇒ 81X = 405
⇒X= =5
... Length of the parallel sides is 4X=4 × 5 =20 cm and 5X = 5 × 5 = 25 cm.
Therefore lengths of the parallel sides are 20 cm, 25 cm.
7. Question
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 two parallel sides.
Answer
Given
Let length of first parallel side X
Length of other parallel side is X + 6
Area of trapezium= 180 cm2
Let Height (h) =9 cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium is × (X + 6 +X) × 9 =180 cm2.
× (X + 6 +X) × 9 =180
⇒ × (2X + 6) × 9 =180
⇒ 2X + 6 =
⇒ 2X + 6 = 40
⇒2X = 40 – 6 =34
⇒X = 17
... Length of the parallel sides is X=17 cm and X + 6 = 17 + 6 = 23 cm.
Therefore lengths of the parallel sides are 17 cm, 23 cm.
8. Question
In a trapezium-shaped field, one of the parallel sides is twice the other. If the area of the field is 9450 m2 and
the perpendicular distance between the two parallel sides is 84 m, find the length of the longer of the parallel
sides.
Answer
Given
Exercise 18A
1. Question
Find the area of a trapezium whose parallel sides are 24 cm and 20 cm and the distance between them is 15
cm.
Answer
Given:
Length of parallel sides is 24cm and 20 cm
Height (h) = 15 cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore, Area of trapezium = × (24 +20) × 15 =330 cm2.
2. Question
Find the area of a trapezium whose parallel sides are 38.7 cm and 22.3 cm, and the distance between them
is 16 cm.
Answer
Given
Length of parallel sides is 38.7cm and 22.3 cm
Height (h) = 16 cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium = × (38.7 +22.3) × 16 = 488 cm2.
3. Question
The shape of the top surface of a table is trapezium. Its parallel sides are 1 m and 1.4 m and the
perpendicular distance between them is 0.9 cm. Find its area.
Answer
Given
Length of parallel sides is 1m and 1.4m
Height (h) = 0.9m
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium = × (1 +1.4) × 0.9
=1.08 m 2.
4. Question
The area of a trapezium is 1080 cm2. If the lengths of its parallel sides be 55 cm and 35 cm, find the distance
,between them.
Answer
Given
Length of parallel sides is 55cm and 35 cm
Area of trapezium= 1080 cm2
Let Height (h) =y cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium is × (55 + 35) × y =1080 cm2.
× (90) × y =1080
⇒ 45 × y =1080
⇒y= = 24
... Distance between the parallel lines is 24 cm.
5. Question
A field is in the form of a trapezium. Its area is 1586 m 2 and the distance between its parallel sides is 26 m. If
one of the parallel sides is 84 m, find the other.
Answer
Given
Let length of parallel sides be 84cm and y cm
Area of trapezium= 1586 cm2
Let Height (h) =26 cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium is × (84 +y) × 26 =1586 cm2.
× (84 +y) × 26 =1586
⇒(84 + y) × 13 =1586
⇒ 84 + y =
⇒ y =122— 84 = 38
... Length of the other parallel side is 38 cm.
6. Question
The area of a trapezium is 405 cm2. Its parallel sides are in the ration 4:5 and the distance between them is
18 cm. Find the length of each of the parallel sides.
Answer
Given
Lengths of the parallel sides are in the ratio 4:5
Therefore let one of the side length be 4X and other side length be 5X
, Area of trapezium= 405 cm2
Let Height (h) =18 cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium is x (4X +5X) × 18 =405 cm2.
× (4X + 5X) × 18 =405
⇒(9X) × 9 =405
⇒ 81X = 405
⇒X= =5
... Length of the parallel sides is 4X=4 × 5 =20 cm and 5X = 5 × 5 = 25 cm.
Therefore lengths of the parallel sides are 20 cm, 25 cm.
7. Question
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 two parallel sides.
Answer
Given
Let length of first parallel side X
Length of other parallel side is X + 6
Area of trapezium= 180 cm2
Let Height (h) =9 cm
We know that area of trapezium is × (sum of parallel sides) × height
Therefore Area of trapezium is × (X + 6 +X) × 9 =180 cm2.
× (X + 6 +X) × 9 =180
⇒ × (2X + 6) × 9 =180
⇒ 2X + 6 =
⇒ 2X + 6 = 40
⇒2X = 40 – 6 =34
⇒X = 17
... Length of the parallel sides is X=17 cm and X + 6 = 17 + 6 = 23 cm.
Therefore lengths of the parallel sides are 17 cm, 23 cm.
8. Question
In a trapezium-shaped field, one of the parallel sides is twice the other. If the area of the field is 9450 m2 and
the perpendicular distance between the two parallel sides is 84 m, find the length of the longer of the parallel
sides.
Answer
Given
