Find the area of a quadrilateral ABCD in which AB = 6 cm, BC = 8 cm, CD = 8 cm, DA = 10 cm and AC = 10 cm. [3 MARKS]

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Solution

Concept : 0.5 Marks
Application : 0.5 Marks
Calculations : 2 Marks

Δ ABC

S= $\frac{P e r i m e t e r}{2}$ = $\frac{(10 + 8 + 6)}{2}$ =12cm

Area= $\sqrt{s (s - a) (s - b) (s - c)}$

= $\sqrt{12 (12 - 10) (12 - 8) (12 - 6)}$

= $\sqrt{576}$ = 24 $c m^{2}$

Now take ΔCDA

S= $\frac{P e r i m e t e r}{2}$ = $\frac{(10 + 8 + 10)}{2}$ =14cm

Area= $\sqrt{s (s - a) (s - b) (s - c)}$

= $\sqrt{14 (14 - 10) (14 - 8) (14 - 10)}$ = $\sqrt{1344}$ = 6.66 $c m^{2}$

Area of Quadrilateral = 24 + 36.66 = 60.66 $c m^{2}$

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Similar questions

In a quadrilateral ABCD AB = 6 cm, BC = 8 cm, CD = 8 cm and AC=10cm.The area of the quadrilateral is 60.67 cm². Find DA.
[4 MARKS]

A B C D

A B = 3 c m

B C = 4 c m

C D = 4 c m

D A = 5 c m

A C = 5 c m

A B C D

A B = 4.2 c m, B C = 6 c m, C D = 5.2 c m, D A = 5 c m

A C = 8 c m

Find the area of the quadrilateral $A B C D$ in which $A B = 3 c m, B C = 4 c m, C D = 4 c m, D A = 5 c m$ and $A C = 5 c m$ .

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