Question

In the figure, ABCD is a quadrilateral, DE and BF are perpendicu-
lars from D and B on AC. If AC = 44 cm, DE = 15 cm and
BF = 20 cm, find the area of the quadrilateral.
E
А
17
1cm​

Answer 1

Answer:

$\huge\colorbox{yellow}{Given\:-}$

AC = 44 cm

DE = 15 cm

BF = 20 cm

$\huge\colorbox{yellow}{To\:Find}$

Area of quadrilateral ABCD

$\huge\colorbox{yellow}{Solution\:-}$

$\small\underbrace\mathrm\red{Using\:formula}$

$\boxed{Area\:of\:triangle = \frac{1}{2} \times b \times h}$

Now,

In Δ ABC

$ar(ABC) = \frac{1}{2} \times b \times h$

$= \frac{1}{2} \times 20 \times 44$

$= > 440 \: {cm}^{2}$

In Δ ACD

$ar(ACD) = \frac{1}{2} \times DE \times AC$

$= \frac{1}{2} \times 15 \times 44$

$= > 330 \: {cm}^{2}$

So, Area of quadrilateral

$ar(ABC) + ar(ACD)$

$440 + 330$

$11(40 + 30)$

$= 11 \times (70)$

$\pink{ = > 770 \: {cm}^{2}}$

Hence, ar(ABCD) = 770 cm^2

$\huge\colorbox{yellow}{Thank\:You}$

$we \: value \: your \: care$

Answer 2

Step-by-step explanation:

=> 770 cm2 this is answer