Question

Construct a quadrilateral $MATH$ with $MA=4cm,AT=3.6cm,TH=4.5cm$, $MH=5cm$ and $\angle A={85}^{\circ }$. Also find its area.

Answer 1

Given:
$\begin{array}{cc}& MA=4cm,AT=3.6cm\\ & TH=4.5cm,MH=5cm\text{and}\angle A={85}^{\circ }\end{array}$
Steps:
1. Draw a line segment $MA=4cm$.
2. Make $\angle A={85}^{\circ }$.
3. With $A$ as centre, draw an arc of radius $3.6cm$. Let it cut the ray $AX$ at $T$.
4. With $M$ and $T$ as centres, draw arcs of radii $5cm$ and $4.5cm$ respectively and let them cut at $H$.
5. Join $MH$ and $TH$.
6. $MATH$ is the required quadrilateral.
Calculation of Area:
Area of the quadrilateral $MATH=\frac{1}{2}\times d\times (h_1+h_2)$ sq. units
$\begin{array}{cc}& =\frac{1}{2}\times 5.1\times (3.9+2.8)\\ & =2.55\times 6.7=17.09{cm}^2\end{array}$