Question

In a quadrilateral ABCD, the diagonal AC = 18 m and the perpendiculars from B and D to
AC are 11 m and 9 m respectively. Calculate the area of the quadrilateral.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that, In a quadrilateral ABCD, the diagonal AC = 18 m and the perpendiculars from B and D to AC are 11 m and 9 m respectively.

Let assume that BE and DF are perpendiculars drawn from B and D on diagonal AC.

So, we have

AC = 18 m

BE = 11 m

DF = 9 m

We know,

Area of quadrilateral is given by

$\boxed{\rm{  \:Area_{(quadrilateral)} = \frac{1}{2}(sum \: of \: perpendiculars) \times diagonal \: }}$

So, on substituting the values, we get

$\rm \: Area_{(quadrilateral)} = \dfrac{1}{2} \times (BE + DF) \times AC$

$\rm \: Area_{(quadrilateral)} = \dfrac{1}{2} \times (11 + 9) \times 18$

$\rm \: Area_{(quadrilateral)} = 20 \times 9$

$\rm\implies \:Area_{(quadrilateral)} = 180 \: {m}^{2}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

PROVIDED INFORMATION :-

• In a quadrilateral ABCD, the diagonal AC = 18 m and the perpendiculars from B and D to AC are 11 m and 9 m

QUESTION :-

• In a quadrilateral ABCD, the diagonal AC = 18 m and the perpendiculars from B and D to AC are 11 m and 9 m respectively. Calculate the area of the quadrilateral.

GIVEN :-

• Diagonal = 18m

• Length of perpendicular from B = 11m

• to D = 9 m

TO FIND :-

• the area of quadrilateral ABCD = ?

SOLUTION :-

Area of quadrilateral = Area of triangle

ABC + Area of triangle ADC

= (1/2 AC × 11) + ( 1/2 × 9 × AC)

= ( 1/2 × 18 × 11) + ( 1/2 × 18 × 9)

= 99 +81

= 180 m²

hence, area of ABCD = 180m²