GED Mathematical Reasoning
Area & Perimeter
Perimeter is the distance all the way around the outside — the fence around a yard. Area is how much surface is inside — the grass that needs mowing. Perimeter is measured in feet; area is measured in square feet, because you are counting squares.
The words first
- perimeter
- the total distance around the outside edge
- area
- the amount of flat surface inside, counted in squares
- base and height
- for a triangle, the bottom and the straight-up distance to the tip
- radius / diameter
- center to edge / all the way across a circle
The method
RECTANGLE
perimeter = add all four sides = 2 × length + 2 × width
area = length × width
TRIANGLE
area = ½ × base × height
(the height is straight up, not the slanted side)
CIRCLE
circumference (the way around) = 2 × π × radius
area = π × radius²
diameter = 2 × radius, so radius = diameter ÷ 2
ODD SHAPES — cut them into rectangles, find each area, add them up.
Worked all the way through
The problem
A rectangular garden is 12 feet long and 7 feet wide. How much fencing goes around it, and how much soil covers it?
- Step 1 — Fencing means the distance around, so perimeter.Two long sides and two short sides: 12 + 12 + 7 + 7
- Step 2 — Add.12 + 12 = 24, and 7 + 7 = 14, so 24 + 14 = 38 feet of fencing.
- Step 3 — Soil covers the inside, so area.area = length × width = 12 × 7
- Step 4 — Multiply.12 × 7 = 84 square feet.
On the board
P = 12 + 12 + 7 + 7
all four sides
P = 24 + 14
P = 38 ft
the fencing
A = 12 × 7
length × width
A = 84 sq ft
the soil
Answer
38 feet of fencing, 84 square feet of soil
A second one, in a different form
A triangle has a base of 10 in and a height of 6 in. What is its area?
A = ½ × base × height
the formula
A = ½ × 10 × 6
A = ½ × 60
A = 30 sq in
half, because a triangle is half a rectangle
Answer
30 square inches
The usual mistake
Squaring the diameter instead of the radius, and dropping the ½ on triangles.
Check yourself
Units tell you if you picked the right formula: fencing comes out in feet, covering comes out in square feet. If your area answer is not in square units, you did a perimeter.
Practice it
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