Question

7. Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm
and AC = 5 cm.
(a) 15 cm
(b) 15.4 cm (c) 15.2 cm (d) none of these​

Answer 1

Answer:

option (c): 15.2 cm

Step-by-step explanation:

AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm

and AC = 5 cm.

divide the quadrilaterals by it diagnol AC

semi perimeter of triangle ABC = (3+4+5)/2 = 6 cm.

semi perimeter of triangle ADC = (5+4+5)/2 = 7 cm

area of quadrilateral = area of triangle ABC + area of triangle ADC

=√6(6-3)(6-5)(6-4) + √7(7-5)(7-4)(7-5)                     (by heron's formula)

=√6×3×1×2   + √7×2×3×2

=2×3  +    2√21

= 6 + 2√21 = 6 + 2×4.582 = 6 + 9.16 = 15.2 cm^2