Question

find the area of quadrilateral abcd ab =9m, bc = 40m, cd = 28m, ad =15m and triangle abc =90degree

Answer 1

the answer is 306m square as you can she in the upper side of photo.if you like this solution then please give me a like

Answer 2

Area of Quadrilateral is 306 $m^2$

Step-by-step explanation:

In quad. ABCD,

AB = 9m, BC = 40m, CD= 28m, AD = 15m

$\angle ABC$ = 90 °

Now in ABC,

$AC^2 = AB^2 + BC^2$

= $(9)^2 + (40)^2$

= 81 + 1600

= 1681

AC = $\sqrt 1681$ = 41 m

∴Area of quad.ABCD = Area of ΔABC+Area of ΔACD

Ar(ABC) = $\frac {1}{2} \times base \times altitude$ (Refer Figure)

= $\frac {1}{2} \times 9 \times 40$

= 180 $m^2$ ""(1)

Ar(ACD) = Applying Heron's Formula

Semiperimeter, s = $\frac {a+b+c}{2}$

= $\frac {15+28+41}{2}$ (Side are 15m, 28m, 41 m)

= 42 m

Area = $\sqrt {s(s-a)(s-b)(s-c)}$

= $\sqrt {42(42-15)(42-28)(42-41)}$

= $\sqrt {42 \times 27 \times 14 \times 1}$

= 126 $m^2$ """(2)

As Area of quad.ABCD = Area of ΔABC+Area of ΔACD

= 180 + 126 (From (1) & (2))

= 306 $m^2$

Area of Quadrilateral is 306 $m^2$