Question

Construct a quadrilateral ABCD with AB = 6 cm, BC = 4 cm, CD = 5 cm, DA = 4.5 cm, EABC = 100 and find its area.

Answer 1

Given:
AB = 6 cm, BC = 4 cm, CD = 5 cm, DA = 4.5 cm $\angle$ ABC = ${100}^o$ .
Steps for construction
Step 1 : Draw a rough diagram and mark the given measurments.
Step 2 : Draw a line segment BC = 4 cm.
Step 3 : At B on $\overline{BC}$ make $\angle$ CBX whose measure is ${100}^o$ .
Step 4 : With B as centre and radius 6 cm draw an arc. This cuts $\overline{BX}$at A. Join $\overline{CA}$
Step 5 : With C and A as centres, draw arcs of radii 5 cm and 4.5 cm respectively and let them cut at D.
Step 6 : Join $\overline{CD}$and $\overline{AD}$ . ABCD is the required quadrilateral.
Step 7 : From B draw $\overline{BF}\perp \overline{AC}$ and from D draw $\overline{DE}\perp \overline{AC}$ . Measure the lengths of BF and DE. BF = $h_1$ = 3 cm, DE = $h_2$ = 2.7 cm and AC = d = 7.8 cm.
Calculation of area:
In the quadrilateral ABCD, d = 7.8 cm, $h_1$ = 3 cm and $h_2$ = 2.7 cm.
Area of the quadrilateral ABCD = $\frac{1}{2}d(h_1+h_2)$
=$\frac{1}{2}\left(7.8\right)(3+2.7)$
=$\frac{1}{2}\times 7.8\times 5.7$
=22.23 $c{m}^2$