Chapter 11.2, Problem 32WE

(a)

To determine

To Find: The area of parallelogram $PQRS$ .

Answer to Problem 32WE

  $A=480sq.unit$

Explanation of Solution

Given:

  

Area of parallelogram $PQRS$

  $\begin{array}{l}b=30\\ h=16\\ A=bh\\ A=(30)(16)\\ A=480sq.unit\end{array}$

Hence, $A=480sq.unit$

(b)

To determine

To Find: The area of triangle $PSR$ .

Answer to Problem 32WE

  $A=240sq.unit$

Explanation of Solution

Given:

  

Area of triangle $PSR$

  $\begin{array}{l}b=30\\ h=16\\ A=\frac{1}{2}bh\\ A=\frac{1}{2}(30)(16)\\ A=240sq.unit\end{array}$

Hence, $A=240sq.unit$

(c)

To determine

To Find: The area of triangle $OSR$ .

Answer to Problem 32WE

  $A(OSR)=120sq.unit$

Explanation of Solution

Given:

  

Area of triangle $OSR$

Since $O$ is the midpoint of $PR$

Thus

  $OP=OR$

Now area of $OSR$ = $\frac{1}{2}$ of area $PSR$

  $\begin{array}{l}A(OSR)=\frac{1}{2}A(PSR)\\ A(OSR)=\frac{1}{2}(240)\\ A(OSR)=120sq.unit\end{array}$

Hence, $A(OSR)=120sq.unit$

(d)

To determine

To Find: The area of triangle $PSO$ .

Answer to Problem 32WE

  $A(PSO)=120sq.unit$

Explanation of Solution

Given:

  

Area of triangle $PSO$

Since $O$ is the midpoint of $PR$

Thus

  $OP=OR$

Now area of $PSO$ = $\frac{1}{2}$ of area $PSR$

  $\begin{array}{l}A(PSO)=\frac{1}{2}A(PSR)\\ A(PSO)=\frac{1}{2}(240)\\ A(PSO)=120sq.unit\end{array}$

Hence, $A(PSO)=120sq.unit$

(e)

To determine

To Find: What must be the area of $POQ$ be? What must be the area of $OQR$ be?

Answer to Problem 32WE

  $A(POQ)=A(OQR)=120sq.unit$

Explanation of Solution

Given:

  

Since

  $\Delta POQ\cong \Delta ORS$

Thus

  $A(POQ)=A(ORS)=120sq.unit$

Similarly

  $\Delta OQR\cong \Delta OPS$

  $A(OQR)=A(OPS)=120sq.unit$

Hence, $A(POQ)=A(OQR)=120sq.unit$

(e)

To determine

To State: What you have seen in part (a) and (e) about how the diagonals divide the parallelogram.

Answer to Problem 32WE

The diagonals of a parallelogram divide it into four equal triangles.

Explanation of Solution

Given:

  

The diagonals of a parallelogram divide it into four equal triangles.