Question

Find the altitude of a trapezium the sum of the lengths of whose bases is 6.5cm and whose area is 23cm​?

Answer 1

Given:

• The sum of the length of the bases of the trapezium is 6.5cm

Thus, the sum of the parallel side of the trapezium is 6.5cm

• Also, the area of the trapezium is 23cm sq.

To find:

The altitude of the trapezium

The formula used to find the area of a trapezium when parallel side and value of altitude is given,

$\boxed{\red{\sf{=\frac{1}{2}\times(sum\ of\ two\ parallel\ side) \times altitude}}}$

So,

We can get the value of the altitude bu using the above formula,

Now,

$\implies \sf{\frac{1}{2}\times(sum\ of\ two\ parallel\ side) \times altitude=23}$

[As given in the question that 'the sum of the parallel side are 6.5cm' we can put the value]

$\implies \sf{\frac{1}{2}\times(6.5) \times altitude=23}$

$\implies \sf{\frac{6.5}{2} \times altitude=23}$

$\implies \sf{ altitude=23 \div \frac{6.5}{2}}$

[By transporting 6.5/2 to RHS]

$\implies \sf{ altitude=23 \times \frac{2}{6.5}}$

$\implies \sf{ altitude= \frac{46}{6.5}}$

$\implies \sf{ altitude= 7.07 cm$

Therefore,

The altitude of the trapezium is 7.07 cm

- - -

Verification,

$\boxed{\red{\sf{=\frac{1}{2}\times(sum\ of\ two\ parallel\ side) \times altitude}}}$

$=\frac{1}{2}\times(6.5) \times 7.07$

$=\frac{45.95}{2}$

= 22.97

Approximately 23 cm sq.