Question

Two parallel sides of trapezium are 24 cm and 52 cm and other sides are 26 cm and 30 cm find the area of the trapezium.

Answer 1

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Answer 2

The area of the trapezium is 912 cm².

Given:

• Two parallel sides of the trapezium are 24 cm and 52 cm and,
• The other sides are 26 cm and 30 cm.

To find:

• Find the area of the trapezium.

Solution:

Formula to be used:

• Area of triangle: $\bf Ar(\triangle) = \sqrt{s(s - a)(s - b)(s - c)}$
• Area of parallelogram$\bf = Base \times Height$
• Area of trapezium $\bf = \frac{1}{2} ( \text{\bf Sum of parallel sides) } \times Altitude$

Step 1:

Draw a parallel line as shown in the figure attached.

Draw a line segment CB parallel to AD .

Now Trapezium ABGD divides into two parts.

A parallelogram ABCD and a triangle BCG.

To find the area of trapezium, we have to calculate height/Altitude of trapezium.

Step 2:

Calculate the area of triangle BCG.

As, Length of sides of triangle are 26,28 and 30 cm.

Apply Heron's formula.

$s = \frac{26 + 28 + 30}{2}$

$\bf s = 42$

$Ar(\triangle) = \sqrt{42(42 - 26)(42 - 28)(42 - 30)}$

$Ar(\triangle) = \sqrt{42 \times 12 \times 14 \times 16}$

$Ar(\triangle) = \sqrt{6 \times 7 \times 6 \times 2 \times 7 \times 2 \times {4}^{2} }$

$Ar(\triangle) = \sqrt{ {6}^{2} \times {7}^{2} \times {4}^{2} \times {2}^{2} }$

$Ar(\triangle) = 6 \times 7 \times 4 \times 2$

$\bf Ar(\triangle) = 336 \: {cm}^{2}$

We know that,

Area of triangle $\bf = \frac{1}{2} \times Base \times Height$

Calculate the area again, with respect to base(CG), Thus

$\frac{1}{2} \times 28 \times BE = 336$

$BE = \frac{336 \times 2}{28}$

$\bf BE = 24 \: cm$

The altitude/height of the triangle is 24 cm.

Thus,

The altitude of the trapezium is 24 cm.

Step 3:

Calculate the area of trapezium.

Now,

We can directly find the area of trapezium using

$\frac{1}{2} ( DG+AB) \times BE$

$= \frac{1}{2} (24 + 52) \times 24$

$= \frac{1}{2} \times 76 \times 24$

$= 38 \times 24$

$\bf Ar.( ABGD)= 912 \: {cm}^{2}$

Alternatively:

Area of trapezium: Area of triangle+ Area of parallelogram

Area of parallelogram $= DC \times BE$

$= 24 \times 24$

$= 576\:cm^2$

Area of trapezium$= 336 +576$

$= 336 + 576$

Area of trapezium$\bf = 912 \: {cm}^{2}$

Thus,

The area of the trapezium is 912 cm².

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