Question

Which of the following is true about the above quadrilateral?

• A. Area of quadrilateral can be calculated by one general formula of area of triangle
• B. Area of quadrilateral cannot be calculate by the general formula of area of triangle because of the absence of height
• C. Height is AD and BC in $△ADC$ and $△ABC$ respectively.
• D. Area of Quadrilateral can be easily calculated by the heron's formula.

Answer 1

Answer: (B), (D)

Area of quadrilateral cannot be calculate by the general formula of area of triangle because of the absence of height
Area of Quadrilateral can be easily calculated by the heron's formula.

If $ABCD$ is a quadrilateral, $AB=3$ cm, $AD=5$ cm, $BC=4$ cm and $CD=4$ cm and $AC=5$ cm.

Area of $ABCD$= Area of triangle $ACD+$Area of triangle $ACB$

In $△ACD$,

$S=\frac{5+5+4}{2}=\frac{14}{2}=7$ cm

Now area of $△ACD$ is:

$A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{7(7-5)(7-5)(7-4)}=\sqrt{7\times 2\times 2\times 3}=\sqrt{84}=2\sqrt{21}$ cm${}^2$

In $△ACB$,

$S=\frac{3+4+5}{2}=\frac{12}{2}=6$ cm

Now area of $△ACB$ is:

$A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{6(6-3)(6-4)(6-5)}=\sqrt{6\times 3\times 2\times 1}=\sqrt{36}=6$ cm${}^2$

Hence, area of quadrilateral $ABCD$ is $(6+2\sqrt{21})$ cm${}^2$.

Area of quadrilateral $ABCD$ cannot be found by the general formula of area of triangle because the height is not given.