Exercise 2.3 (Area of the Trapezium)

Exercise 2.3

1. Find the missing values.

(i) Height h = 10 m

Parallel sides a = 12m, b = 20 m

Area of the trapezium = 1/2 h (a + b) sq. units

                                    = 1/2 × 10 (12 + 20) sq.m

                                   = 5 × 32 sq.m = 160 sq.m

(ii) Height h = ?

Parallel sides a = 13 cm, b = 28 cm

Area of the trapezium = 1/2 h(a + b) = 492 sq.cm

                                   = 1/2 h (13 + 28) = 492

                                   = 1/2 h × 41 = 492

                                h = 492 / 41 × 2 = 24 cm

                    Height h = 24 cm

(iii) Height h = 19 m

Parallel sides a = ?, b = 16 m

 Area = 323 sq.m

 1/2 h×(a + b) = 323 sq.m

 1/2 × 19 (a + 16) = 323

 a + 16 = [ 323 × 2 ] / 19 = 34

 a = 34 – 16 = 18 m

 a = 18 m

(iii) Height h = 16 cm

Parallel sides a = 15cm, b = ?

 Area = 360 sq.cm

 1/2 h×(a + b) = 360 sq.cm

 1/2 × 16 (15 + b) = 360

 15 + b = [ 360 × 2 ] / 16 = 45

 b = 34 – 15 = 30 cm

 a = 30 cm

2. Find the area of a trapezium whose parallel sides are 24 cm and 20 cm and the distance between them is 15 cm.

Parallel sides a = 24 cm, b = 20 cm

                           Height h = 15 cm

Area of the trapezium = 1/2 h (a + b) sq.units

Area of the trapezium = 1/2 × 15 (24 + 20) sq. units

                                   = 1/2 × 15 × 44 sq.cm

                                  = 330 sq.cm

Area of the trapezium = 330 sq.cm

3. The area of a trapezium is 1586 sq. cm. The distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm then, find the other side.

Area of the trapezium = 1586 sq. cm

 Height h = 26 cm

One of the parallel sides a = 84 cm

The other side b = ?

1/2 h (a + b) = 1586

 1/2 × 26 (84 + b) = 1586

  84 + b = 1586 / 13 = 122

 b = 122 – 84 = 38 cm

The other side = 38 cm

4. The area of a trapezium is 1080 sq. cm. If the lengths of its parallel sides are 55.6 cm and 34.4 cm, find the distance between them.

The area of the trapezium = 1080 sq.cm

Parallel sides a = 55.6cm

                  b = 34.4 cm

      Height h = ?

1/2 h (a + b) = 1080

1/2 h (55.6+ 3.4) = 1080

 ½ h × 90.0 = 1080

 h =1080 / 45 = 24 cm.

The distance between them = 24 cm

5. The area of a trapezium is 180 sq. cm and its height is 9 cm. If one of the parallel sides is longer than the other by 6 cm, find the length of the parallel sides.

The area of the trapezium = 180 sq. cm

 Height h = 9 cm

 Parallel sides a =  x cm

                     b = x + 6 cm

Area of the trapezium = 1/2 h (a + b) = 180

                                  = 1/2 × 9(x + x + 6) = 180

                                 = 1/2 × 9 (2x + 6) = 180

                               = 2x + 6 = ( 180 / 9) × 2 = 40

 2x = 40 – 6 = 34

 x = 34 / 2 = 17

 x = 17

 a = 17 cm

 b = (17 + 6) cm

 = 23 cm

The length of the parallel sides = 17 cm, 23 cm.

6. The sunshade of a window is in the form of isosceles trapezium whose parallel sides are 81 cm and 64 cm and the distance between them is 6 cm. Find the cost of painting the surface at the rate of ₹ 2 per sq. cm.

The parallel sides a = 81cm, b = 64 cm

                 Height h = 6 cm

Area of isosceles trapezium = 1/2 h (a + b) sq. units

                                            = 1/2 × 6 (81+ 64) sq.cm

                                          = 3 × 145 sq.cm

                                       = 435 sq.cm

Cost of painting per sq. cm = ₹ 2

Cost of painting 435 sq. cm = ₹ 435 × 2 = 870

Cost of painting the surface = ₹ 870 

7. A window is in the form of trapezium whose parallel sides are 105 cm and 50 cm respectively and the distance between the parallel sides is 60 cm. Find the cost of the glass used to cover the window at the rate of ₹ 15 per 100 sq. cm.

The parallel sides a = 105 cm, b = 50 cm

                   Height h = 60 cm

Area of the trapezium = 1/2 h (a + b) sq.units

 = 1/2 × 60 (105+ 50) sq.cm

= 30 × 155 sq.cm

= 4650 sq.cm      

Cost of the glass used to cover 100 sq.cm = ₹ 15

Cost of the glass used to cover 4650 sq.cm = [ ₹ 15 × 4650 ] /100

= ₹ 6975 / 10 = ₹ 697.50

The cost of the glass used to cover the window = ₹ 697.50

Objective type questions

8. The area of the trapezium, if the parallel sides are measuring 8 cm and 10 cm and the height 5 cm is

(i) 45 sq. cm

(ii) 40 sq. cm

(iii) 18 sq. cm

(iv) 50 sq. cm

Answer : (i) 45 sq cm

9. In a trapezium if the sum of the parallel sides is 10 m and the area is 140 sq. m, then the height is

(i) 7cm

(ii) 40 cm

(iii) 14 cm

(iv) 28 cm

Answer : (iv) 28 cm

10. when the non-parallel sides of a trapezium are equal then it is known as

(i) a square

(ii) a rectangle

(iii) an isosceles trapezium

(iv) a parallelogram

Answer : (iii) an isosceles trapezium

ANSWERS

Exercise 2.3

1. (i) 160 sq.cm (ii) 24 cm (iii) 18 m (iv) 30 cm

2. 330 sq.cm

3. 38 cm

4. 24 cm

5. 23 cm and 17 cm

6. ₹ 870

7. ₹ 697.50

 Objective type questions

8. (i) 45 sq.cm

9. (iv) 28 cm

10. (iii) isosceles trapezium