Trapezium | MCQs

Explanation

Area = 1/2 × (sum of bases) × altitude

48 = 1/2 × (14 + 18) × altitude

48 = 1/2 × 32 × altitude

48 = 16 × altitude

Altitude = 48/16 = 3 cm.

Explanation

Given:

Area = 42 cm²

Bases: a = 4.6 cm, b = 2.4 cm

Area formula: Area = (1/2) × (a + b) × h

42 = (1/2) × (4.6 + 2.4) × h

42 = (1/2) × 7 × h

42 = 3.5 × h

h = 42 / 3.5

h = 12

Explanation

1/2 (sum of parallel sides × altitude) formula is derived from the fact that a trapezium can be divided into a rectangle and a triangle. 

The area of the trapezium is the sum of the areas of these two shapes, which simplifies to 1/2 × (a + b) × h, where a and b are the lengths of the parallel sides, and h is the altitude.

Explanation

Given:

Area = 42 cm² (assuming the unit is consistent, but it's given as m² which seems incorrect given the base lengths are in cm. Let's proceed with cm² for calculation purposes)

Bases:

a = 5.6 cm

b = 2.9 cm

Formula:

Area = ((a + b) / 2) × height

42 = ((5.6 + 2.9) / 2) × height

42 = (8.5 / 2) × height

42 = 4.25 × height

height = 42 / 4.25

height = 9.88 cm

Explanation

The area of a trapezium is given by:

Area = (1/2) × (sum of bases) × altitude

Given:

Area = 153 m^2

Altitude = 9 m

One base = 13 m

Let's denote the other base as 'b'. Then:

153 = (1/2) × (13 + b) × 9

Multiply both sides by 2:

306 = (13 + b) × 9

Divide both sides by 9:

34 = 13 + b

Subtract 13 from both sides:

b = 21