Area & Perimeter Flashcards

All 22 cards in this deck

What is the perimeter of a 2D shape?

The total distance around the outside of the shape.

What is the formula for the perimeter of a rectangle?

e.g. a rectangle 5 cm by 3 cm

$P = 2(l + w)$

e.g. $2(5+3) = 16$ cm

On a rectilinear (L-shaped) shape, how do you find a missing horizontal side length?

Subtract the other horizontal lengths from the longest horizontal side.

e.g. $10 - 4 = 6$ cm

True or false? When a composite shape is split into rectangles, the lines drawn inside it count towards the perimeter.

False. Only the outside edges of the shape are added to give the perimeter.

What units is a perimeter measured in?

Units of length, e.g. mm, cm, m — never squared units.

What are the steps to find the side lengths of a rectangle from its perimeter when the sides are algebraic?

e.g. sides $x+1$ and $2x$ cm, perimeter 20 cm

1. Write the perimeter as an expression: $2(x+1+2x) = 20$
2. Solve the equation: $6x + 2 = 20$, so $x = 3$
3. Substitute back: sides are 4 cm and 6 cm

What is the formula for the area of a triangle?

$A = \frac{1}{2} \times \text{base} \times \text{perpendicular height}$

What is the formula for the area of a parallelogram?

$A = \text{base} \times \text{perpendicular height}$

What is the formula for the area of a trapezium?

$A = \frac{1}{2}(a+b)h$, where $a$ and $b$ are the parallel sides and $h$ is the perpendicular distance between them.

True or false? To find the area of a parallelogram you multiply two adjacent side lengths.

False. You multiply the base by the perpendicular height, not by the slant side.

What are the steps to find the height of a triangle when its area and base are known?

e.g. area $24$ cm², base $6$ cm

1. Substitute into the formula: $24 = \frac{1}{2} \times 6 \times h$
2. Simplify: $3h = 24$
3. Divide: $h = 8$ cm

How many square centimetres are there in $1\text{ m}^2$?

$10\,000$, since $100 \times 100 = 10\,000$.

What is a composite shape?

A shape made up of two or more basic shapes joined together.

What are the two ways of finding the area of an L-shaped shape?

Split it into rectangles and add the areas; or find the area of the surrounding rectangle and subtract the missing piece.

What are the steps to find the area of a composite shape by adding areas?

e.g. a shape split into a 5 cm by 2 cm rectangle and a 3 cm by 2 cm rectangle

1. Split the shape into basic shapes: two rectangles
2. Find each area: $10$ cm² and $6$ cm²
3. Add them: $16$ cm²

What are the steps to find a shaded area when a smaller shape is cut out of a larger one?

e.g. a 3 cm by 2 cm rectangle removed from a 10 cm by 6 cm rectangle

1. Area of the whole outer shape: $60$ cm²
2. Area of the piece removed: $6$ cm²
3. Subtract: shaded area $= 54$ cm²

True or false? When a shape is split into two parts, the area of the whole shape is the sum of the areas of the two parts.

True. Areas of the separate pieces add to give the total area.

True or false? If a semicircle sits on the 10 cm side of a rectangle, so that side is its diameter, its area is $\frac{1}{2}\pi \times 10^2$.

False. The radius is half the diameter, so the area is $\frac{1}{2}\pi \times 5^2$.

What are the steps to form an equation from a given area with algebraic sides?

e.g. a square of side $(x+3)$ cm has area $10$ cm²

1. Write the area as an expression: $(x+3)(x+3) = 10$
2. Expand: $x^2 + 6x + 9 = 10$
3. Rearrange ready to solve: $x^2 + 6x = 1$

True or false? On a scale drawing where 1 cm represents 5 m, an area of 1 cm² on the drawing represents 5 m² in real life.

False. It represents $5^2 = 25$ m².

If the lengths in an area problem are given in mixed units (e.g. cm and m), what must you do first?

Convert all the lengths to the same unit before calculating the area.

True or false? Two rectangles with the same perimeter must have the same area.

False. Equal perimeters can give different areas (and equal areas can give different perimeters).