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Geometry

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Perimeter The perimeter is the distance around a two-dimensional object. The perimeter of a polygon can always be calculated by adding all the length of the sides together.

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Perimeter Square = 4S The perimeter of a square is the distance around the outside of the square. A square has four sides of equal length. The formula for finding the perimeter of a square is: 4S (Length of a Side)

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**Perimeter Square Example:**

Find the perimeter of a square with sides that measure 25 m. Solution: P = 4S P = 4 (25m) P = 100 m So, the perimeter is 100 m.

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Perimeter Rectangle 2L + 2W or 2 (L + W) L = Length W= Width

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**Perimeter Rectangle Example:**

Find the perimeter of a rectangular field of length 45 m and width 35 m. Solution: P = 2 (L + W) P = 2 ( ) P = 2 (80) P = 160 So, the perimeter is 160 m.

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**Circumference Circle Circumference = 2π r Circumference = π d**

P stands for the perimeter, r stands for the radius π is the mathematical constant pi (π = ) d stands for the circle's diameter (twice the radius of a circle)

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Circumference Circle

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**Circumference Example:**

The diameter of a circle is 3 centimeters. What is the circumference? Circumference = π d = 3.14 · (3 cm) = 9.42 cm

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**Area Area is a count of how many unit squares fit inside a figure.**

The solution is labeled using square units.

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Area of a Square The area A of any square is equal to the square of the length s of a side. Formula: A = s2

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Area of a Rectangle The area A of any rectangle is equal to the product of the length l and the width w. Formula: A = lw or A = bh

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Area of a Triangle The area A of any triangle is equal to one-half the product of any base b and corresponding height h. Formula: A = 1/2bh

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Area of a Trapezoid The area A of any trapezoid is equal to one-half the product of the height h and the sum of the bases, b1 and b2. Formula: A = 1/2h(b1 + b2)

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Area of a Circle The area A of any circle is equal to the product of PI and the square of the radius r. Formula: A = (PI)r2

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