Question

Find the area and the perimeter of quadrilateral ABCD, given below; if AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and ∠DBC = 90°.

Answer 1

Given, AB = 8 cm, AD = 10 cm, BD = 12 cm, DC = 13 cm and ∠DBC = 90^°

BC = `sqrt("DC"^2 - "BD"^2)`

= `sqrt( 13^2 - 12^2 )`

= 5 cm

Hence, perimeter = 8 + 10 + 13 + 5 = 36 cm

Area of ΔABD, `sqrt("s"("s"-"a")("s"-"b")("s"-"c"))`

Here, s = `("a"+"b"+"c")/2`

= `(10+12+8)/2` 

= `30/2`

= 15 cm

ΔABD = `sqrt( 15( 15 - 8 )( 15 - 10 )( 15 - 12 ))`

= `sqrt( 15 xx 7 xx 5 xx 3 )`

= `15sqrt7`

= 39.7

Area of ΔBDC,

ΔBDC = `1/2` × 12 × 5

= 30

Now,

Area of ABCD = area of ΔABD + area of ΔBDC

= 39.7 + 30

= 69.7 sq.cm