Question

look at the measures shown in the adjacent figure and find the area of quadrilateral PQRS.

Answer 1

Answer:

The area of quadrilateral PQRS is 690 m².

Step-by-step explanation:

Triangle PSR is a right angle triangle. The area of triangle PSR is

$A=\frac{1}{2}\times base\times height$

$Area(PSR)=\frac{1}{2}\times 15\times 36=270$

The area of triangle PSR is 270 m².

Using Pythagoras theorem,

$PR^2=PS^2+SR^2$

$PR^2=(36)^2+(15)^2$

$PR=39$

The length of PR is 39 m.

Use heron's formula, the area of a triangle is

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

Where, $s=\frac{a+b+c}{2}$.

In triangle PQR,

$s=\frac{56+25+39}{2}=\frac{120}{2}=60$

The area of triangle PQR is

$A=\sqrt{60(60-56)(60-25)(60-39)}$

$A=\sqrt{60(4)(35)(21)}$

$A=\sqrt{176400}$

$Area(PQR)=420$

The area of triangle PQR is 420 m².

The area of quadrilateral PQRS is the sum of area of triangle PSR and triangle PQR.

$Area(PQRS)=Area(PSR)+Area(PQR)$

$Area(PQRS)=270+420=690$

Therefore the area of PQRS is  690 m².

Answer 2

Answer:

Area of PQRS is 690

${m}^{2}$