Question

Find the area of a quadrilateral ABCD in which AB=16cm, BC=CD=26cm, AD=12cm and the diagonal BD= 20cm

Answer 1

Step-by-step explanation:

......................

Answer 2

Answer:

336 cm²

Step-by-step explanation:

Observe the diagram of the question above

We will find the area of ▢ ABCD by finding the area of 2 triangles

∴ According to heron's formula

area of triangle =

semiperimeter (s) of triangle =

$\frac{a + b + c}{2}$

and Area of triangle =

$\sqrt{s(s - a)(s - b)(s - c)}$

's' stands for semiperimeter and a , b , c stands for the sides of triangle

this formula is used when we know the three sides of a triangle

∴ Area of Δ ABD

s = a + b+ c / 2

= 12 + 16 + 20 /2

= 48 /2

= 24

and now area of trianlge =

$\sqrt{s(s - a)(s - b)(s - c)}$

=

$\sqrt{24(24 - 12)(24 - 16)(24 - 20)}$

when we solve this we will get

area = 96 cm²

similarly we can find the area of Δ BCD

and we will get area as 240 cm²

now area of ▢ ABCD = A Δ ABD + A Δ BCD

= 96 + 240

= 336 cm²