Question

ABCD is a trapezium in which AB ∥ CD, AD ⊥ DC, AB = 4 cm, BP = 7 cm and DC = 25 cm, then area of the trapezium is 45.

Answer 1

Question:

ABCD is a trapezium in which AB ∥ CD, AD ⊥ DC, AB = 4 cm, BP = 7 cm and DC = 25 cm, then area of the trapezium is ____.

Answer:

101.5cm²

Step-by-step explanation:

The figure for the trapezium ABCD is attached to this response.

To find the area of the trapezium, we use the formula for calculating the area of a trapezium given as follows;

A  = $\frac{1}{2}$ x (a + b) x h            ------------------(i)

Where;

A = area of the trapezium

a and b are the parallel sides of the trapezium

h = height of the trapezium.

As shown in the figure,

AB and CD are parallel

Therefore, we can say that;

a = AB

b = CD

Also, from the figure,

The height of the trapezium is BP

Therefore, we can say that;

h = BP

We know that;

a = AB = 4cm

b = CD = 25cm

h = BP = 7cm

Substitute these values of a, b and h into equation (i) as follows;

A  = $\frac{1}{2}$ x (4 + 25) x 7    

A  = $\frac{1}{2}$ x (29) x 7    

A = 101.5

Therefore, the area of the trapezium is 101.5cm²