Question

Construct a trapezium BOAT in which $\overline{BO}$ is parallel to $\overline{TA},BO=7cm,OA=6cm,$ $BA=10cm$ and $TA=6cm$. Also find its area.

Answer 1

Given:
$\begin{array}{cc}& BO=7cm,OA=6cm,BA=10cm,\\ & TA=6cm\text{and}\overline{BO}\parallel \overline{TA}\end{array}$
Steps:
1. Draw a line segment $BO=7cm$.
2. With B and $O$ as centres, draw arcs of radii $10cm$ and $6cm$ respectively and let them cut at $A$.
3. Join BA and OA.
4. Draw AX parallel to $BO$
5. With $A$ as centre, draw an arc of radius $6cm$ cutting $AX$ at $T$.
6. Join BT. BOAT is the required trapezium.
Calculation of Area:
$\begin{array}{cc}\text{Area of the trapezium BOAT}& =\frac{1}{2}\times h\times (a+b)\text{sq.units}\\ & =\frac{1}{2}\times 5.9\times (7+6)=38.35sq.cm\end{array}$