9.4 Use properties of rectangles, triangles, and trapezoids  (Page 5/17)

The perimeter of a rectangular swimming pool is $150$ feet. The length is $15$ feet more than the width. Find the length and width.

Solution

Step 1. Read the problem. Draw the figure and label it with the given information.
Step 2. Identify what you are looking for.	the length and width of the pool
Step 3. Name. Choose a variable to represent it. The length is 15 feet more than the width.	Let $W=\text{width}$ $W+15=\text{length}$
Step 4. Translate. Write the appropriate formula and substitute.
Step 5. Solve the equation.
Step 6. Check:
Step 7. Answer the question.	The length of the pool is 45 feet and the width is 30 feet.

Got questions? Get instant answers now!

Got questions? Get instant answers now!

Use the properties of triangles

We now know how to find the area of a rectangle. We can use this fact to help us visualize the formula for the area of a triangle. In the rectangle in [link] , we’ve labeled the length $b$ and the width $h,$ so it’s area is $bh.$

We can divide this rectangle into two congruent triangles ( [link] ). Triangles that are congruent have identical side lengths and angles, and so their areas are equal. The area of each triangle is one-half the area of the rectangle, or $\frac{1}{2}bh.$ This example helps us see why the formula for the area of a triangle is $A=\frac{1}{2}bh.$

The formula for the area of a triangle is $A=\frac{1}{2}bh,$ where $b$ is the base and $h$ is the height.

To find the area of the triangle, you need to know its base and height. The base is the length of one side of the triangle, usually the side at the bottom. The height is the length of the line that connects the base to the opposite vertex, and makes a $\text{90°}$ angle with the base. [link] shows three triangles with the base and height of each marked.

Triangle properties

For any triangle $\text{Δ}ABC,$ the sum of the measures of the angles is $\text{180°}.$

$m\text{∠}A+m\text{∠}B+m\text{∠}C=\text{180°}$

The perimeter of a triangle is the sum of the lengths of the sides.

$P=a+b+c$

The area of a triangle is one-half the base, $b,$ times the height, $h.$

$A=\frac{1}{2}bh$

Find the area of a triangle whose base is $11$ inches and whose height is $8$ inches.

Solution

Step 1. Read the problem. Draw the figure and label it with the given information.
Step 2. Identify what you are looking for.	the area of the triangle
Step 3. Name. Choose a variable to represent it.	let A = area of the triangle
Step 4. Translate. Write the appropriate formula. Substitute.
Step 5. Solve the equation.
Step 6. Check:
Step 7. Answer the question.	The area is 44 square inches.

Got questions? Get instant answers now!

Got questions? Get instant answers now!