PERIMETER AND AREA BASICS |

**Perimeter: Getting Around the Outside**

The Perimeter of a figure is the **distance **or measure** around the outside**.

**length **and** width** are sometimes called **base **and** height**.

To find the perimeter of a rectangle or square, we could add all the sides, but we could also take a shortcut since we know that pairs of sides in the rectangle and all sides in the square are equal.

A **rectangle's** **perimeter** (P) equals **the sum** of the **length** (*l*) **and** the **width** (*w*)** times 2**.

**P = 2 × length + 2 × width = 2 × ( length + width ) = 2 × ( l + w )**

For a **square**, the perimeter (P) equals** ****4*** ***times the length** of any **side** (*s*).

**P = 4 × side length = 4s**

For an irregular figure**, Perimeter** = the **sum **of the **lengths** of all the sides.

**Examples:**

1) The Perimeter of:

a) a parallelogram (//gm) with **2 sides = 7 in** and **2 sides = 9 in**. is 2 (7 + 9) = **32 inches**.

b) a **rectangle** with **length** (*l*) = **14 ft.** and **width** (*w*) = **10 ft.** is 2 (14 + 10) = 2 (24) = **48 feet.**

c) A **Square** with **side** (*s*) = **12 yards** is 4 (12) = **48 yards**.

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**Area: Covering Up the Inside**

The things we use -- like paint, wallpaper and tiles -- to cover surfaces like walls and floors are always **measured and priced** in **square units**. The information on every paint can label includes the number of square feet or square meters of space, the paint will cover.

The **measure of the surface** covered by a closed figure is called **AREA**.

We measure area in **SQUARE UNITS** -- square inches, square feet, square miles --

because, to measure the area of a figure, we "*square it off*" and then count the squares.

We indicate or write square units like this: units², inches², ft².

There's a shortcut for finding the area of a rectangle or a square.

For a **rectangle** the ** Area = length times width**.

*A = l × w*

For a **square**, ** Area = the square of the side length**.

*A = s × s = s²*

For an **irregular figure**, we **count** the **squares**.

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Now get a pencil, an eraser and a note book, copy the questions,

do the practice exercise(s), then check your work with the solutions.

If you get stuck, review the examples in the lesson, then try again.

**Practice Exercises**

1) Find the perimeter of the figures below. Use the shortcut formula when you can.

2) Find the area of the figures above. Use the shortcut formula when you can.

3) Maria and her mother are making a tablecloth for a rectangular **table** that is **3 feet long
**and

a) What is the area of the tabletop?

b) What are the length and width of the tablecloth? (hint: draw the cloth as a rectangle)

c) What is the area of the tablecloth?

d) What is the difference between the area of the table and tablecloth?

e) What length of lace should Maria's mom buy to sew a lace trim all around

the outside edge of the cloth?

**Solutions**

1) a) A rectangle that is 4 units by 5 units. **P = 2 (4 + 5) = 18 units**.

b) A square that is 3 units per side. **P = 4 × 3 = 12 units**.

c) irregular shape,** count steps** around the outside = **22 units**.

d) irregular shape, **count steps** around the outside = **21 units**. (2 half steps make a whole on top)

2) a) A rectangle that is 4 units by 5 units. **A = 4 × 5 = 20 square units**.

b) A square that is 3 units per side. **A = 3 × 3 = 3² = 9 square units**.

c) irregular shape, **count** squares: **A = 12 square units**.

d) irregular shape, **count** squares: **A = 13 square units**.

3)

a) What is the area of the tabletop? **6 square feet**

b) What are the length and width of the tablecloth? add 2 feet to each side: **5 ft. by 4 ft.**

c) What is the area of the tablecloth? **20 square feet**

d) The difference in the areas = 20 square feet - 6 square feet = **14 square feet**.

e) length of lace she should buy = perimeter of the cloth = **2 (4 + 5) = 18 feet**** **of lace.

( *Plane Geometry MathRoom Index* )

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