Question

In quadrilateral $ABCD$, if $AB=7cm,BC=12cm,CD=12cm,DA=9cm$ and diagonal $AC=15cm$. What is its area>

• A. $(10\sqrt{17}+54)sqcm$
• B. $(10\sqrt{34}-54)sqcm$
• C. Data insufficient
• D. None of these

Answer 1

Answer: (A)

$(10\sqrt{17}+54)sqcm$

R.E.F image

$ar\left(ABCD\right)=ar\left(ABC\right)+ar\left(ACD\right)$

for $\Delta \left(ADC\right)$

Use heron's formula

$S=\frac{15+12+9}{2}=18cm$

$ar\left(ABC\right)=\sqrt{S(S-a)(S-b)(S-c)}$

$ar\left(ABC\right)=\sqrt{18\times 3\times 6\times 9}=54cm$

||ly for $\Delta \left(ACB\right)$

$S=\frac{15+12+7}{2}=17$

$ar\left(ABC\right)=\sqrt{17\times (17-15)(17-12)(17-7)}=10\sqrt{17}c{m}^2$

$\Rightarrow ar\left(ABCD\right)=(10\sqrt{17}+54)c{m}^2$