Question

In a quadrilateral ABCD AB is equal to 28 CM BC is equal to 26 CM CD is equal to 50 cm DC is equal to 40 cm and diagonal AC is equal to 30 cm find the area of the quadrilateral

Answer 1

In triangle ABC

Area (ABC) = 1/2 * 28 * 26
                     = 364 Cm^2

in triangle ADC

Area (ADC) = 1/2 * 40 * 50
                    = 1000 Cm^2

Area =  1000 + 364
         =  1364 Cm^2

Answer 2

Solution :-

There is a mistake in this question. CD = 50 cm and again DC = 40 cm. I think it should be DA = 40 cm

In quadrilateral ABCD, there are two triangles - Δ ADC and Δ ABC and AC is the common side of these two triangles.

Using Heron's formula of area of triangle = √s(s - a)(s - b)(s - c)

In Δ ADC -

Semi perimeter = s = (a + b + c)/2

⇒ s = (40 + 50 + 30)/2

⇒ s = (120/2)

⇒ s = 60 cm

In Δ ABC -

s = (28 + 26 + 30)/2

⇒ s = 84/2

s = 42 cm

Area of Δ ADC = √60(60 - 40)(60 - 50)(60 - 30)

⇒ √60*20*10*30

⇒ √360000

Area of Δ ADC = 600 cm²

Area of triangle Δ ABC = √ 42(42 - 28)(42 - 26)(42 - 30)

⇒ √ 42*14*16*12

⇒ √112896

Area of Δ ABC = 336 cm²

Area of quadrilateral ABCD = Area of Δ ADC + Area of Δ ABC

⇒ 600 cm² + 336 cm²

= 936 cm²

So, area of quadrilateral ABCD is 936 cm²