Question

Find the area of quadrilateral PQRS in which PQ is 5cm ,QR is 12cm,RS is 10cm,SP is 13cmand PR is 13 cm​

Answer 1

Firstly devide that quadrilateral in two triangles and then find out the area of both the triangles by heron's formula and then add the areas of both the triangles

Heron's Formula =√s(s-a)(s-b)(s-c)

Here, s= half of perimeter of triangle

a,b,c =sides of triangles......

Answer 2

ANSWER: $\sqrt{90}$

step-by-step explanation

In ∆PQR

perimeter=13+12+5=30

s- semi perimeter = $\cancel\frac{30}{2}$=15cm

AREA OF TRIANGLE PQR=$\sqrt{s(s-a)(s-b)(s-c)}$

=$\sqrt{15(15-13)(15-12)(15-5)}$

=$\sqrt{15 X 2 X 3 X 10}$

=$\sqrt{3 X 5 X 2 X 3 X 5 X 2}$

=$\sqrt{2X5X3}$

=$\sqrt{30}$${cm^3}$

NOW In ∆RSP

perimeter=13+13+10=36

s- semi perimeter = $\cancel\frac{36}{2}$=18cm

=$\sqrt{18(18-13)(18-13)(18-10)}$

=$\sqrt{18 X 5 X 5 X 8}$

=$\sqrt{2 X 3 X 3 X 5 X 5 X 2 X 2 X 2}$

=$\sqrt{2 X 2 X 3 X 5}$

=$\sqrt{60}$${cm^3}$

ADDING AREA OF ∆PQR AND ∆RSP

$\sqrt{30}$+$\sqrt{60}$

=$\sqrt{90}$${CM^3}$