Question

Find the area of a quadrilateral PQRS, if its sides are consecutively 3 cm, 4 cm, 4 cm and 5 cm with diagonal PR = 5 cm.

Answer 1

{(a+b) / 2}*h = (3+5)/2 * 3 = 12

Answer 2

Answer:

Area of Quadrilateral PQRS = 15.16 cm²

Step-by-step explanation:

As per the given question,

First draw the quadrilateral PQRS, as shown below

By Heron’s formula,

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

Where s = half of the perimeter of triangle

In ΔPQR

s = (3+4+5)/2 =6

$Area PQR\ =\sqrt{6(6-3)(6-4)(6-5)}$

$Area PQR =\sqrt{36}$

Area PQR = 6 cm²

In ΔPSR

s = (5+4+5)/2 = 7

$Area PQR\ =\sqrt{7(7-5)(7-4)(7-5)}$

$Area PQR =\sqrt{84}$

Area PQR = 9.165 cm²

Therefore,

Area of Quadrilateral PQRS = Area of ΔPQR +  Area of ΔPSR

= 6 + 9.165

= 15.16 cm²

Hence, the Area of Quadrilateral PQRS = 15.16 cm²