Question

find the area of a quadrilateral ABCD in which AB=3 cm , BC=4 cm , DA=5 cm, and AC = 5cm

Answer 1

Answer:

17 cm × 360 = 45575 0 and your answer comes

Answer 2

Given:

AB = 3cm

BC = 4cm

DA = 5cm  

AC = 5 cm  

To find:

We need to find the Area of a Quadrilateral.

Solution:

First, we need to divide the quadrilateral into two triangles by using Hero's formula and calculate the area of triangle.

Heron's formula for the area of a triangle is: Area = $\sqrt{S (S - a) (S - b) (S - c)}$

Here, S be the Semi perimeter.

First we need to find the ΔABC,  

AB²  +BC²= 3² + 4²

                = 9 + 16

                = 25

∴AC² = 5²

Since ∆ABC obeys the Pythagoras theorem, we can say ∆ABC is right-angled at B.

Therefore, the area of ΔABC = 1/2 × base × height

= 1/2 × 3 cm × 4 cm = 6 cm²

Area of ΔABC = 6 cm²

Now, We need to consider the  ∆ADC

We will consider a = 5 cm, b = 4 cm and c = 5 cm

Semi Perimeter: s = $\frac{Perimeter}{2}$

∴ S = $\frac{a + b+ c}{2}$

      = $\frac{5 + 4+ 5}{2}$

      = $\frac{14}{2}$

      = 7

∴ Semi perimeter = 7 cm

By using Heron’s formula,

Area of ΔADC = $\sqrt{S (S-a) (S-b) (S-c)}$  

Here, put S = 7 in the above equation

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

= $\sqrt{7(2)(3)(2)}$

= $\sqrt{84}$

= 9.2cm²(approximate value)

Area of ΔADC = 9.2cm²

∴Area of the quadrilateral ABCD = Area of ΔADC + Area of ΔABC

                                                      = 9.2 cm² + 6cm²

                                                      = 15.2 cm²

Therefore, the Area of the quadrilateral ABCD is 15.2 cm².