Review: GED math area and perimeter

Definition of area

Area measures the space inside a shape, often in square units.

Definition of perimeter

Perimeter is the total distance around a shape, measured in linear units.

True or false: Area is always larger than perimeter.

False, because area can be smaller than perimeter for some shapes.

Fill in the blank: The perimeter of a rectangle is _____.

The perimeter of a rectangle is $\displaystyle 2(l + w)$, where l is length and w is width.

Calculate the area of a rectangle: 5m x 3m

Area = $\displaystyle 5m \times 3m = 15m^2$.

Perimeter formula for a square

The perimeter of a square is $\displaystyle P = 4s$, where s is the side length.

Difference between area and perimeter

Area measures space; perimeter measures distance around a shape.

What is the area of a triangle with base 4m and height 3m?

Area = $\displaystyle \\frac{1}{2} \times base \times height = \\frac{1}{2} \times 4m \times 3m = 6m^2$.

Calculate the perimeter of a rectangle: length 7m, width 2m.

Perimeter = $\displaystyle 2(7m + 2m) = 18m$.

True or false: A circle has a perimeter.

False, circles have a circumference, not a perimeter.

What is the formula for the area of a circle?

Area = $\displaystyle \pi r^2$, where r is the radius.

Which is larger for a given square, area or perimeter?

Area grows faster than perimeter as the side length increases.

Fill in the blank: The area of a circle with radius 2m is _____.

Area = $\displaystyle \pi \times (2m)^2 = 4\pi m^2 \approx 12.57m^2$.

True or false: Rectangle perimeter is additive.

True, because you can add side lengths to find perimeter.

Example of area in real life: garden size

The area of a garden helps determine how many plants can fit.

What affects the perimeter of a shape?

Changing any side length affects the perimeter.

Calculate the area of a square with side 4m.

Area = $\displaystyle s^2 = 4m \times 4m = 16m^2$.

Perimeter of a triangle with sides 3m, 4m, 5m

Perimeter = $\displaystyle 3m + 4m + 5m = 12m$.