Question

The figure alongside shows a trapezium ABCD in which AB||DC, <D = 90°, CD = 24 cm, AC = 26 cm and AB = 18 cm. Find the area of the trapezium.​

Answer 1

Answer:

• Given the dimension of a trapezium except the height✓

Firstly we need to. calculate out the height of the trapezium so as to find the area of the trapezium ✓

From the above information we find that ADC forms a right angle triangle and Right angled at D

$\bold{so \: by \: applying \: pythagoras \: theorem \: we \: can\: find \: the \: height\: f \: the \: triangle \: }$

$= > ac ^{2} \: = ad^{2} + dc^{2} \\ \\ = > 26 ^{2} = 24^{2} + ad ^{2} \\ \\ = > ad = \sqrt{26 ^{2} - 24 ^{2} } \\ \\ = > ad = \sqrt{676 - 576} \\ \\ = > ad = \sqrt{100} = 10 \: cm$

So from the above calculation we find the height of the triangle is 10 cm And it's clear that the height of the triangle is equal to the height of the trapezium

So the area if the trapezium is as follows

$\bold{\red{\: area = \frac{1}{2} \times (ab \: + dc) \times ad }}\\ \\ = >area = \frac{(18 + 24) \times 10}{2} \\ \\ = > area = \frac{420}{2} \\ \\ = > \bold{\boxed{\red{\boxed{area \: = 210cm ^{2} }}}}$

So the area if the trapezium is 210 cm²