Question

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

Answer 1

Answer:

find the area of quadrilateral ABCD in which ab is equal to 3 cm BC is equal to 4 cm CD is equal to 4 cm BC is equal to 5 cm and ac is equal to 5 cm find the area by heron's formula heroines formula

Answer 2

Area of quadrilateral ABCD=$15.16 cm^2$

Step-by-step explanation:

Area quadrilateral ABCD=Area(ΔABC)+Area(ΔADC)

By Heron's Formula,

$Area (\Delta ABC)= \sqrt {s(s-a)(s-b)(s-c)}$

Here $s=\frac{a+b+c}{2}$

        $s=\frac{5+5+4}{2}$

        $s=\frac{14}{2}$

        s=7 cm

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

$Area( \Delta ABC)=\sqrt{7\times 2\times 2 \times3}$

$Area(\Delta ABC)=2\sqrt{21}$

Area$(\Delta ABC)$=$2 \times {4.58}$

Area(\Delta ABC) =$9.16 cm^2$

Similarly,

$Area(\Delta ACD)=\sqrt{s(s-a)(s-b)(s-c)}$

Here $s=\frac{a+b+c}{2}$

        $s=\frac{3+5+4}{2}$

       $s=\frac{12}{2}$

        s=6 cm

$Area(\Delta ACD)=\sqrt{6(6-5)(6-3)(6-4)]$

$Area(\Delta ACD)=\sqrt{6\times 1\times 3 \times 2}$

$Area(\Delta ACD)=\sqrt{6\times 6}$

Area(ΔACD)=6

Area(ΔACD)=$6 cm^2$

Now,Area of quadrilateral ABCD=Area(ΔABC)+Area(ΔACD)

                                                       =$9.16 cm^2+ 6 cm^2$

                                                       =$15.16 cm^2$