Question

Construct a quadrilateral ABCD with AB = 4 cm, BC = 6 cm, CD = 5.6 cm DA = 5 cm and AC = 8 cm. Find also its area.

Answer 1

Given: AB = 4 cm, BC = 6 cm, CD = 5.6 cm, DA = 5 cm and AC = 8 cm.
To construct a quadrilateral
Steps for construction
Step 1 : Draw a rough figure and mark the given measurements.
Step 2 : Draw a line segment AB = 4 cm.
Step 3 : With A and B as centres draw arcs of radii 8 cm and 6 cm respectively and let them cut at C.
Step 4 : Join $\overline{AC}$ and $\overline{BC}$
Step 5 : With A and C as centres draw arcs of radii 5 cm, and 5.6 cm respectively and let them cut at D.
Step 6 : Join $\overline{AD}$ and $\overline{CD}$ . ABCD is the required quadrilateral.
Step 7 : From B draw $\overline{BE}\perp \overline{AC}$ and from D draw $\overline{DF}\perp \overline{AC}$, then measure the lengths of BE and DF. BE = $h_1$ = 3 cm and DF = $h_2$ = 3.5 cm.
AC = d = 8 cm.

Calculation of area:
In the quadrilateral ABCD, d = 8 cm, $h_1$ = 3 cm and $h_2$ = 3.5 cm.
Area of the quadrilateral ABCD = $\frac{1}{2}d(h_1+h_2)$

$=\frac{1}{2}\left(8\right)(3+3.5)$

$=\frac{1}{2}\times 8\times 6.5$

$=26c{m}^2$