Question

Find the area of a quadrilateral ABCD whose sides are AB = 8 cm, BC = 15 cm, CD = 12 cm AD = 25 cm and angle B is 90 degree, using quadrilateral formula​

Answer 1

Answer:

answer

Step-by-step explanation:

ab+bc+cd+da=360°

Answer 2

Area of Quadrilateral is 150 $cm^2$

Step-by-step explanation:

In right ΔABC,

$AB^2 + BC^2 = AD^2$

$AC^2 = 15^2 + 8^2$

AC = $\sqrt {15^2 + 8^2}$

= $\sqrt {225 + 64}$

= $\sqrt 289$

= 17 cm

Length of AC = 17 cm

Area of ΔABC = $\frac {1}{2} (8 \times 15)$

= 60 cm^2

Now, In ΔACD, AD = 25 cm, AC = 17 cm & CD = 12 cm

Using Heron's Formula, semiperimeter, $s = \frac {a + b + c}{2}$

= $\frac {17+12+25}{2}$

= $\frac {54}{2}$

= 27 cm

Length of AD = 27 cm

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

= $\sqrt {27(27-17)(27-12)(27-25)}$

= $\sqrt {27 \times 10 \times 15 \times 2}$

= $\sqrt {3 \times 3 \times 3 \times 2 \times 5 \times 3 \times 5 \times 2}$

= $3 \times 3 \times 2 \times 5$

= 90 $cm^2$

Hence, Area of Quadrilateral ABCD = Area of ΔABC + Area of ΔACD

= 60 + 90  

= 150 $cm^2$