PERIMETER BASICS
What is the perimeter of a square with side length 8?
Answer: 32 units (8+8+8+8 or 4×8)
What is the formula for the area of a rectangle?
Answer: length × width (or l × w)
What is the formula for the area of a triangle?
Answer: ½ × base × height (or ½bh)
You're putting a fence around a square garden with 15-foot sides. How much fencing do you need?
Answer: 60 feet
TRUE or FALSE: Perimeter is measured in SQUARE units.
Answer: FALSE (perimeter uses regular units like feet, inches; AREA uses square units)
A rectangle is 12 feet long and 5 feet wide. What's the perimeter?
Answer: 34 feet (12+5+12+5)
A square has a side length of 9 inches. What's the area?
Answer: 81 square inches (9×9)
A right triangle has base 8 and height 6. What's the area?
Answer: 24 square units (½×8×6)
You're buying carpet for a 10 ft × 12 ft room. How many square feet of carpet do you need?
Answer: 120 square feet
Name ONE situation where you'd need to know PERIMETER and ONE situation where you'd need AREA.
Answer: Perimeter - fencing, framing, borders; Area - carpet, paint, tile (accept reasonable answers)
A triangle has sides 7 cm, 9 cm, and 11 cm. What's the perimeter?
Answer: 27 cm
A rectangle has length 15 and width 8. What's the area?
Answer: 120 square units
A triangle has base 14 cm and height 10 cm. What's the area?
Answer: 70 square cm
You're painting a triangular wall with base 16 feet and height 8 feet. One can of paint covers 50 square feet. How many cans do you need?
Answer: 2 cans (area = 64 square feet, so need 2 cans)
Which shape gives you MORE area: a 10×10 square or a 20×5 rectangle? Show your work!
Answer: Same area! Both = 100 square units
An L-shaped figure has these outer edges: 10, 6, 4, 3, 6, 9. What's the perimeter?
Answer: 38 units
Two rectangles: Rectangle A is 10×6, Rectangle B is 8×8. Which has MORE area and by how much?
Answer: Rectangle B has more; B=64, A=60, difference = 4 square units
A right triangle has legs of 12 feet and 16 feet. If you wanted to find the perimeter, what additional information do you need?
Answer: The length of the hypotenuse (the third side) - or need to use Pythagorean theorem
You have 40 feet of rope to make a rectangular dog pen. If you make it 12 feet long, how wide will it be? What's the area?
Answer: Width = 8 feet (perimeter: 12+w+12+w=40), Area = 96 square feet
CHALLENGE: A rectangular garden has perimeter 48 feet and length 16 feet. What's the width? What's the area?
Answer: Width = 8 feet (16+w+16+w=48, so 2w=16), Area = 128 square feet
A composite figure is made of a rectangle (15 × 8) with a square (side 5) cut out of one corner. What's the PERIMETER of the remaining shape?
Answer: 56 units (original rectangle perimeter 46, minus one corner where square was 10, plus the two new edges inside where square was cut 10, total adds 56)
Alternative simpler answer: Count all outer edges: 15, 8, 10, 5, 5, 3, 3, 8 = 56
A rectangle has area 96 square feet and width 8 feet. What's the length? What's the perimeter?
Answer: Length = 12 feet (96÷8), Perimeter = 40 feet (12+8+12+8)
A composite figure is made of a rectangle (10 × 6) and a right triangle attached to one of the short sides (base 6, height 8). What's the TOTAL area?
Answer: 84 square units (rectangle: 60 + triangle: 24 = 84)
You need to create a triangular garlic powder safe zone with area of AT LEAST 100 square feet to escape an effeminate vampire with sparkly skin. If your base is 20 feet, what's the MINIMUM height you need? Show your work!
Answer: 10 feet (100 = ½ × 20 × h, so 100 = 10h, h = 10)
ULTIMATE CHALLENGE: You have exactly 36 feet of fencing to make a rectangular garden. What dimensions give you the MAXIMUM area? What is that maximum area?
Answer: 9 feet × 9 feet (a square), Maximum area = 81 square feet
Note: Students should test a few rectangles and discover square gives max area