Question

Construct a trapezium ABCD with dimensions $AB=8cm,BC=5cm,AC=6cm,CD=4.5cm$ and AB is parallel to CD. Find the area of the trapezium (in sq cm.).

• A. $23.5$
• B. $22.5$
• C. $26.5$
• D. None of these

Answer 1

The correct option is B $22.5$

$\Rightarrow$ Draw a line segment $AB=8cm$

$\Rightarrow$ Take A as a center with radius $6cm$ and draw an arc.

$\Rightarrow$ Take B as a center with radius $5cm$ and draw an arc meeting previous arc at point $C$.

$\Rightarrow$ Draw a horizontal line passing through a point $C$.

$\Rightarrow$ Cut off line $CD=4.5cm$

$\Rightarrow$ Draw a $CP\parallel AD$

$\Rightarrow$ Measure the length of $CP$.

$\Rightarrow$ $l\left(CP\right)=3.6cm$

$\Rightarrow$ Area of trapezium $ABCD=\frac{AB+CD}{2}\times CP$

$\Rightarrow$ $\frac{8+4.5}{2}\times 3.6$

$\Rightarrow$ $22.5c{m}^2$

$\therefore$ Area of the trapezium is $22.5c{m}^2$.