© by S-Squared, Inc. All Rights Reserved. 1.Find the distance, d, and the midpoint, m, between (4, − 2) and (2, 6) Distance Formula: d = (x 2 – x 1 ) 2 + (y 2 – y 1 ) 2 Substitute Simplify (6 – (− 2)) 2 + (2 – 4) 2 (6 + 2) 2 + (2 – 4) 2 (8) 2 + (− 2)

﴾, ﴿ Find the distance, d, and the midpoint, m, between (4, − 2) and (2, 6) Midpoint Formula: m = ﴾, ﴿ 2 y 1 + y 2 x 1 + x 2 2 Substitute Simplify ﴾, ﴿ 2 − m = ﴾, ﴿ m =

2.Find the perimeter and the area of the given rectangle: 6 cm 14 cm Area = length width Perimeter = 2 length + 2 width Area = 14 6 Substitute Area = 84 cm 2 Perimeter = Perimeter = Perimeter = 40 cm

3.The perimeter of the rectangle below is 54 cm. Find the length. 9 cm l Perimeter = 2 length + 2 width width = 9 length = l Perimeter = 54 Formula Identify variables Substitute 54 = 2 l Simplify 54 = 2 l + 18 – 18 Subtract – = 2 l Divide = l 18cm = length

x = (x + 1) 2 x = (x + 1)(x + 1) 4.Find the two unknown side lengths of the given triangle: x + 1 x 5 ft Hint: Use Pythagorean’s Theorem to find x. a 2 + b 2 = c 2 Note: Identify a, b and c Substitute b = 5 a = x c = x + 1 Simplify Subtract – x 2 – 1 25 = 2x = 2x x = x 2 + 2x + 1 – x 2 Subtract – 1 Divide = x Note: Side lengths are x and x + 1 x = 12 ft x + 1 = 13 ft

5.Find the perimeter and the area of the given rectangle: yd Volume = length width height Volume = Substitute Volume = or yds yds Volume = Note: Turn mixed number to improper fraction Volume = Reduce

6.Find the circumference and the area of the given circle: 7 m Circumference = 2 π r where r is the radius and let π = 3.14 Substitute Circumference = Circumference = Circumference = m Note: Identify r r = 7 Simplify

6.Find the circumference and the area of the given circle: 7 m Area = π r 2 where r is the radius and let π = 3.14 Substitute Area = Area = Area = m 2 Note: Identify r r = 7 Simplify

7.Find the area and perimeter of the given shape: 3 in Since the altitude divides the base of the triangle, which is also a side length of the square, in half each segment is 4 inches. 8 in Hint: The altitude divides the base of the triangle in half 4 in All side lengths of a square are equal so the other side length is 8 inches. 8 in Use the Pythagorean Theorem to find the legs of the triangle = c = c 2 25 = c 2 Substitute Simplify Square Root 5 = c 25 = c 2 5 in

7.Find the area and perimeter of the given shape: 3 in 8 in Hint: The altitude divides the base of the triangle in half 4 in 8 in 5 in Note: Perimeter is distance around Perimeter = Perimeter = Perimeter = Perimeter = Perimeter = 34 in

Note: Area of the shape is the sum of the area of the triangle and the area of the square. 7.Find the area and perimeter of the given shape: 3 in 8 in Hint: The altitude divides the base of the triangle in half 4 in 8 in 5 in Area(square) = 8 2 Area(square) = 64 in 2 Area of the square is s 2 Area of the triangle is b h 2 1 base = 8 height = 3 Area(triangle) = (8)(3) 2 1 Area(triangle) = (4)(3) Area(triangle) = 12 in 2 Area(shape) = Area(shape) = 76 in 2