Question

we have to find the area ​

Answer 1

Answer:

$\sf \green {\therefore \: Area \: of \: quadrilateral \: \sf \green ∆ABCD}$ $= \sf \green {{44 \: cm}^{2}}$

Step-by-step explanation:

$\sf Area \: of \: ∆ADC = \frac{1}{2} \times B \times H$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times (4 + 7) \times 3$

$\sf = \frac{1}{2} \times 11 \times 3 = \frac{1}{2} \times 33 = \frac{33}{2}$

= 16.5 cm²

$\sf Area \: of \: ∆ABH = \frac{1}{2} \times B \times H$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{ \cancel2} \times \cancel {4}^{2} \times 5 = 2 \times 5$

= 10 cm²

$\sf Area \: of \: ∆BHC = \frac{1}{2} \times B \times H$

$\sf \: \: \: \: \: \: \: = \frac{1}{2} \times 7 \times 5 = \frac{1 \times 7 \times 5}{2} = \frac{35}{2}$

= 17.5 cm²

Area of quadrilateral ABCD = Area of ∆ADC + Area of ∆ABH + Area of ∆BHC

= 16.5 cm² + 10 cm² + 17.5 cm²

= 44 cm²