**Geometry Chapter 1.7 Introduction to Perimeter, Circumference, and Area**

**I) Vocabulary and Formulas:**

**Notation:**

**A = Area**

**P = Perimeter**

**A) Triangle:**

A = (1/2)(base)(height)

P = (side a) + (side b) + (side c)

**Example:**Given Triangle ABC with side a = 10, b = 17 and c = 21 and the height of the triangle is 8. Find the area and the perimeter.

Area = (1/2)(21)(8) = 84 square units.

Perimeter = 10 + 17 + 21 = 48 units

**B) Square**: has all the sides equal so the base = height so we will call them all sides.

A = (side)(side) = s

^{2}

P = side + side + side + side = 4s

**Example**: let one side of a square is equal to 5 inches. what is the area and perimeter?

A = (5)

^{2}= 25 square inches

P = 4 (5) = 20 inches

**C) Rectangle**:

A = (base)(height)

P = 2b + 2h

**Example**: let the base = 3 and the height = 4

A = (3)(4) = 12 square units

P = (2)(3) + (2)(4) = 6 + 8 = 14 units

**D) Circle**: 2 radius = diameter

A = π

*r*

^{2}

P = Circumference = 2 π

*r*

**Example**: If a circles diameter is 20 cm, what is the area and circumference?

A = π (10)

^{2}= 100π square cm.

C = (2) π (10) = 20 π cm.