Question

Construct a trapezium ABCD in which $\overline{AB}$ is parallel to $\overline{DC}$ , AB = 10 cm,BC = 5 cm, AC = 8 cm and CD = 6 cm. Find its area.

Answer 1

Given:
$\overline{AB}$ is parallel to $\overline{DC}$, AB = 10 cm, BC = 5 cm, AC = 8 cm and CD = 6 cm.

Steps for construction:
Step 1 : Draw a rough diagram and mark the given measurements.
Step 2 : Draw a line segment AB = 10 cm.
Step 3 : With A and B as centres draw arcs of radii 8 cm and 5 cm respectively and let them cut at C.
Step 4 : Join $\overline{AC}$ and $\overline{BC}$ .
Step 5 : Draw $\overline{CX}$ parallel to $\overline{BA}$ .
Step 6 : With C as centre and radius 6 cm draw an arc cutting $\overline{CX}$ at D.
Step 7 : Join $\overline{AD}$ . ABCD is the required trapezium.
Step 8 : From C draw $\overline{CE}\perp \overline{AB}$ and measure the length of CE. CE = h = 4 cm. AB = a = 10 cm, DC = b = 6 cm.

Calculation of area:
In the trapezium ABCD, a = 10 cm, b = 6 cm and h = 4 cm.
Area of the trapezium ABCD = $\frac{1}{2}$ h(a+b)

$=\frac{1}{2}$ (4)(10+6)

$=\frac{1}{2}\times$ 4 $\times$ 16

$=32c{m}^2$