Chapter 11, Problem 12STP

a.

To determine

The area of the each square and the area of the triangle

Answer to Problem 12STP

The area of the squares are $144{\text{m}}^{\text{2}}$ , $25{\text{m}}^{\text{2}}$ and $169{\text{m}}^{\text{2}}$ and the area of triangle is $30{\text{m}}^{\text{2}}$ .

Explanation of Solution

Given:

The model has three squares of side $12\text{m},5\text{m}\text{and}13\text{m}$ and triangle made by these square sides.

Concept Used:

• The area $A$ of the square of side $a$ is

  $A=a^2$

• The area $A$ of the triangle having base $b$ and height $h$ is

  $A=\frac{1}{2}\times b\times h$

Calculation:

The area $A$ of the square of side $a$ is

  $A=a^2$

• The area of the square of side $a=12m$

  $\begin{array}{l}A={12}^2\\ A=144{\text{m}}^{\text{2}}\end{array}$

• The area of the square of side $a=5\text{m}$

  $\begin{array}{l}A=5^2\\ A=25{\text{m}}^{\text{2}}\end{array}$

• The area of the square of side $a=13\text{m}$

  $\begin{array}{l}A={13}^2\\ A=169{\text{m}}^{\text{2}}\end{array}$

The area $A$ of the triangle having base $b$ and height $h$ is

  $A=\frac{1}{2}\times b\times h$

In the model the sides of squares made a triangle whose base $b=5\text{m}$ and the height $h=12\text{m}$ .

• The area of given triangle is

  $\begin{array}{l}A=\frac{1}{2}\times 5\times 12\\ A=30{\text{m}}^{\text{2}}\end{array}$

Conclusion:

The area of the squares are $144{\text{m}}^{\text{2}}$ , $25{\text{m}}^{\text{2}}$ and $169{\text{m}}^{\text{2}}$ and the area of triangle is $30{\text{m}}^{\text{2}}$

b.

To determine

Total area of the given model

Answer to Problem 12STP

The total area of the given model is $368{\text{m}}^{\text{2}}$

Explanation of Solution

Given:

The model has three squares of side $12\text{m},5\text{m}\text{and}13\text{m}$ and triangle made by these square sides.

Calculation:

The total area of the model is the sum of all the squares and the triangle.

The area of the squares are $144{\text{m}}^{\text{2}}$ , $25{\text{m}}^{\text{2}}$ and $169{\text{m}}^{\text{2}}$ and the area of triangle is $30{\text{m}}^{\text{2}}$

So, the total area of the model is

  $\begin{array}{l}\text{Total}\text{area}=144+25+169+30\\ \text{Total}\text{area}=368{\text{m}}^{\text{2}}\end{array}$

The total area of the model is $368{\text{m}}^{\text{2}}$ .

Conclusion:

The total area of the given model is $368{\text{m}}^{\text{2}}$

c.

To determine

The area of the square model the pythagorean theorem

Answer to Problem 12STP

The area of the square model the pythagorean theorem

Explanation of Solution

Given:

The model has three squares of side $12\text{m},5\text{m}\text{and}13\text{m}$ and triangle made by these square sides.

Concept Used:

Pythagoras theorem:

In a right angle triangle follow as:

  $a^2+b^2=c^2$

Where, the $a$ is base of triangle, $b$ is perpendicular of triangle and $c$ is hypotenuse of triangle.

Calculation:

The sides of the three square are $12\text{m},5\text{m}\text{and}13\text{m}$ forms a triangle.

So, the sides of the triangle is $12\text{m},5\text{m}\text{and}13\text{m}$ .

Check Pythagoras theorem to this triangle

Where base $a=5\text{m}$ and perpendicular $b=12\text{m}$ and hypotenouse $c=13m$

  $\begin{array}{l}{a}^2+b^2=5^2+{12}^2\\ =169\end{array}$

And

  $\begin{array}{l}{c}^2={13}^2\\ =169\end{array}$

Which satisfy the pythagoras theorem.

So, the area of the square model the pythagorean theorem

Conclusion:

The area of the square model the pythagorean theorem