Question

find the area of quadrilateral abcd in which sides ab=7cm,bc=12 cm and da=9cm,cd=12cm and diagnol ac=15​

Answer 1

Answer:

Area of triangle ABC + Area of triangle ADC

First, find the area of the triangles ABC and ADC.

In the triangle ABC,

AB(a)=7cm,BC(b)=12cm and AC(c)=15cm,

s=a+b+c2

Substitute the value of a,b and c into the formula:

s=7+12+152

s=342=17

Now, use the Heron’s formula to find the area of the triangle, which is given as:

Area of triangle ABC=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√

Substitute the values of s,a,b, and c into the formula:

Area of triangle ABC=17(17−7)(17−12)(17−15)−−−−−−−−−−−−−−−−−−−−−−−√

Area of triangle ABC=17×10×5×2−−−−−−−−−−−−√

Area of triangle ABC=1700−−−−√

Area of triangle ABC=1017−−√ cm2

So, the area of the triangle ABC is 1017−−√ cm2

In the triangle ADC,

AD(a)=9cm,DC(b)=12cmandAC(c)=15cm,

s=a+b+c2

Substitute the value of a,b and c into the formula:

s=9+12+152

s=362=18

Now, use the Heron’s formula to find the area of the triangle, which is given as:

Area of triangle ADC=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√

Substitute the values of s,a,b, and cinto the formula:

Area of triangle ADC=18(18−9)(18−12)(18−15)−−−−−−−−−−−−−−−−−−−−−−−√

Area of triangle ADC=18×9×6×3−−−−−−−−−−−√

Area of triangle ADC=2916−−−−√

Area of triangle ADC=54 cm2

The area of the triangle ADC is 54 cm2.

So, the area of the quadrilateral is given as:

∴ The area of quadrilateral=Area of triangle ABC + Area of triangle ADC

The area of quadrilateral =(1017−−√+54) cm2

Therefore, the area of the quadrilateral is (1017−−√+54) cm2.

Note:When we have given the three sides of the triangle then we can use the Heron’s formula to find the area of the triangle and when we have given the base and the height of the triangle then we can use the formula for finding the area:

Area of triangle =12(Base)(Height)