Question

22. Find the perimeter and area of a quadrilateral
ABCD in which BC = 12 cm, CD = 9 cm, BD = 15 cm,
DA = 17 cm and <ABD = 90°.​

Answer 1

Answer:

perimeter=17+9+12+8

=46cm........

Answer 2

Answer:

perimeter = 46cm

area = 114cm^2

Step-by-step explanation:

by Pythagoras theorem

$AB^2 + BD^2 = AD^2 \\ AB^2 = {17}^{2} - {15}^{2} = 289 - 225 = 64 \\ AB = \sqrt{64} = 8cm$

Perimeter = AB + BC+ CD + AD

Perimeter = 8 + 12 + 9 + 17 = 46cm

$area of ABD = \frac{1}{2} \times 8 \times 15 \\ = 60 {cm}^{2}$

$area of BCD \\ = \sqrt{18 (18 - 15)(18 - 12)(18 - 9)} \\ = \sqrt{18 \times 6 \times 3 \times 9} \\ = 6 \times 3 \times 3 = 54 {cm}^{2}$

$total \: area \: = \: (60 + 54) {cm}^{2} = 114 {cm}^{2}$