Question

Look at the measures shown in the adjacent figure and find the area of ☐ PQRS.

Answer 1

Join PR.
In triangle PSR,
Applying Pthygoras theorem,
$$\begin{gathered} {\mathrm{PS}}^2+{\mathrm{SR}}^2={\mathrm{PR}}^2 \\ \Rightarrow {36}^2+{15}^2={\mathrm{PR}}^2 \\ \Rightarrow {\mathrm{PR}}^2=1296+225=1521 \\ \Rightarrow \mathrm{PR}=\sqrt{1521}=39\mathrm{m} \end{gathered}$$
In triangle PQR,
$$\begin{gathered} s=\frac{56+25+39}{2}=60 \\ \mathrm{Area}=\sqrt{60\left(60-56\right)\left(60-25\right)\left(60-39\right)} \\ =\sqrt{60\times 4\times 35\times 21} \\ =\sqrt{176400} \\ =420{\mathrm{m}}^2 \end{gathered}$$
Area of triangle PSR = $\frac{1}{2}\times 15\times 36=270{\mathrm{m}}^2$
Area of PQRS = Area of triangle PSR + Area of triangle PQR
= 270 + 420
= 690 m²