Area & Perimeter Flashcards

All 26 cards in this deck

What is the perimeter of a 2D shape?

The total distance all the way around the outside of the shape (add all the side lengths).

What is the formula for the perimeter of a rectangle?

e.g. a rectangle 7 cm by 3 cm

$P = 2 \times (\text{length} + \text{width})$

e.g. $2 \times (7+3) = 20$ cm

How do you find the side length of a square from its perimeter?

e.g. perimeter $36$ cm

Divide the perimeter by 4.

e.g. $36 \div 4 = 9$ cm

What are the steps to find the perimeter of an L-shape when some side lengths are not labelled?

e.g. an L-shape with labelled sides 10 cm, 7 cm, 5 cm and 4 cm

1. Find the missing lengths from opposite sides: $10-4=6$ and $7-5=2$
2. Add every side once around the outside: $10+7+4+5+6+2$
3. Give the answer in length units: $34$ cm

True or false? Perimeter is measured in square units such as cm$^2$.

False. Perimeter is a length, so it is measured in mm, cm, m etc.; only area uses square units.

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

False. e.g. a $1$ cm by $12$ cm and a $3$ cm by $4$ cm rectangle both have area $12$ cm$^2$ but different perimeters.

What is the formula for the area of a rectangle?

$\text{area} = \text{length} \times \text{width}$

What is the formula for the area of a triangle?

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

What is the formula for the area of a parallelogram?

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

What is the formula for the area of a trapezium?

$\text{area} = \frac{1}{2}(a+b)h$, 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 triangle you multiply the base by a sloping side and halve it.

False. You must use the perpendicular height (the height at right angles to the base), not a sloping side.

How do you find the side length of a square from its area?

e.g. area $81$ cm$^2$

Take the square root of the area.

e.g. $\sqrt{81} = 9$ cm

What is a compound (composite) shape?

A shape made by joining two or more basic shapes, such as rectangles and triangles.

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

e.g. an L-shape split into a 5 cm by 2 cm rectangle and a 3 cm by 4 cm rectangle

1. Split the shape into rectangles (and triangles)
2. Work out each area: $5\times2=10$ and $3\times4=12$
3. Add them: $10+12=22$ cm$^2$

What are the steps to find the area of a shaded region?

e.g. a 10 cm by 6 cm rectangle with a 4 cm by 3 cm rectangle cut out of it

1. Area of the whole shape: $10\times6=60$
2. Area of the unshaded part: $4\times3=12$
3. Subtract: $60-12=48$ cm$^2$

True or false? The area of a compound shape equals the sum of the areas of the parts it is split into.

True. Splitting a shape does not change the total area.

True or false? The perimeter of a shape made from two rectangles joined together is the sum of the two rectangles' perimeters.

False. The joined edges are inside the shape, so they are not part of its perimeter.

True or false? An L-shape's area can be found by subtracting a rectangle from a larger surrounding rectangle.

True. Adding parts or subtracting a missing piece both give the same area.

What are the steps to find the perpendicular height of a triangle from its area?

e.g. area $24$ cm$^2$, base $8$ cm

1. Put the numbers in the formula: $\frac{1}{2}\times8\times h=24$
2. Simplify: $4h=24$
3. Divide: $h=6$ cm

How do you find the perpendicular height of a parallelogram from its area and base?

e.g. area $30$ cm$^2$, base $5$ cm

Divide the area by the base.

e.g. $30 \div 5 = 6$ cm

What are the steps when one shape's area is a given multiple of another's?

e.g. a rectangle of length 16 cm has 6 times the area of a triangle with base 8 cm and height 9 cm — find its width

1. Find the first area: $\frac{1}{2}\times8\times9=36$
2. Multiply by the given number: $6\times36=216$
3. Divide by the known length: $216\div16=13.5$ cm

What are the steps to work out the cost of covering a floor at a price per square metre?

e.g. a floor 6 m by 4 m at £3 per m$^2$

1. Find the area: $6\times4=24$ m$^2$
2. Multiply by the cost per m$^2$: $24\times3$
3. Answer: £72

What are the steps to find $x$ when the sides are given in terms of $x$ and the perimeter is known?

e.g. a rectangle with sides $x+1$ and $2x$, perimeter $26$ cm

1. Write the perimeter in terms of $x$: $2(x+1+2x)=6x+2$
2. Form an equation: $6x+2=26$
3. Solve: $x=4$

How many cm$^2$ are there in $1$ m$^2$?

$10\,000$ cm$^2$, because $1$ m $=100$ cm and $100\times100=10\,000$.

The area of shape A is 5 times the area of shape B. What equation do you write to compare them?

e.g. B is a triangle of area $72$ cm$^2$, A is a parallelogram with base $30$ cm and perpendicular height $h$

area of A $= 5 \times$ area of B

e.g. $30 \times h = 5 \times 72$

True or false? If the side length of a square is doubled, its area is doubled.

False. The area becomes $4$ times as large.