The perimeter is the total distance all the way round the outside of a 2-D shape. It is a length in one dimension, so it is measured in millimetres, centimetres, metres and so on, never in squared units.

How do you find a missing length on the outline of a composite shape?

Compare the horizontal lengths with each other and the vertical lengths with each other, keeping the two directions separate. Add lengths together to find a missing longer side, and subtract them to find a missing shorter one.

What do dashes drawn on two sides of a shape mean?

The two sides are equal in length. So a length given on one of them applies to the other as well, which is often how a diagram supplies a side it never labels.

What is the circumference of a circle?

The circumference is the perimeter of a circle, that is the distance all the way round its edge. It is a length like any other perimeter, so it is added to straight sides directly when a shape contains both.

A shape is made from a quarter circle and two straight sides. What makes up its perimeter?

The curved part plus both straight sides. The curved part is a quarter of the full circumference, and the two straight edges are added on to it, since they are just as much part of the outline.

True or False? Two equal semicircles in one shape have the same total curved length as one full circle.

True. Halving the circumference and then doubling it brings you back to the whole circumference. So you can work out the full circle once and skip the halving altogether, which saves a step and a rounding decision.

True or False? The height used to find the area of a triangle must be the length of one of its sides.

False. It is the perpendicular height, measured at right angles to the base. In many triangles no side runs at right angles to the base, so the height has to be worked out rather than read off the diagram.

What units does an area have?

Square units, such as cm² or m². Two lengths have been multiplied together to reach it, which is what the small 2 is recording, and leaving it off turns an area into a length.

Define composite shape .

A composite shape is one that is not a standard shape in its own right, but can be split into standard shapes. The pieces are usually rectangles, triangles and parts of circles, all of which have area formulae you can use.

How do you find the area of a composite shape?

Split it into standard shapes and work out the area of each one separately. Those separate areas are then combined into a single total, which is the only step where the arrangement of the pieces matters.

How do you find the area of a semicircle or a quarter circle?

Work out the area of the whole circle first, using the radius. Then divide that area by 2 for a semicircle, or by 4 for a quarter circle.

True or False? There is only one correct way to split a composite shape into standard shapes.

False. There is usually more than one, and every split that covers the shape exactly gives the same total area. So it is worth pausing to pick the split that produces the easiest shapes to work with.

National 5MathsSQAApplications of MathematicsFlashcardsGeometric SkillsPerimeter & Area

Perimeter & Area (SQA National 5 Applications of Mathematics): Flashcards

Exam code: X844 75

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Cards in this collection (21)

Define perimeter.
The perimeter is the total distance all the way round the outside of a 2-D shape.
It is a length in one dimension, so it is measured in millimetres, centimetres, metres and so on, never in squared units.
How do you find a missing length on the outline of a composite shape?
Compare the horizontal lengths with each other and the vertical lengths with each other, keeping the two directions separate.
Add lengths together to find a missing longer side, and subtract them to find a missing shorter one.
The longest horizontal side of a logo is 18 cm, and one of the two shorter sides below it is 15 cm. Complete the missing length:
$18 - 15 =______cm$
The completed calculation is:
$18 - 15 = 3 cm$
The two shorter horizontal sides have to add up to the long one, so the missing side is the difference between them.
What do dashes drawn on two sides of a shape mean?
The two sides are equal in length.
So a length given on one of them applies to the other as well, which is often how a diagram supplies a side it never labels.
What is the circumference of a circle?
The circumference is the perimeter of a circle, that is the distance all the way round its edge.
It is a length like any other perimeter, so it is added to straight sides directly when a shape contains both.
You are given the radius of a circle and need its circumference. What must you do first?
Double the radius to get the diameter.
The given formula is $C = π d$ , which uses the diameter, so multiplying the radius by $π$ instead would give exactly half the right answer.
Complete the rule for the curved length of part of a circle:
To get the curved length of a semicircle you divide the full circumference by $______$ and for a quarter circle you divide it by $______$ instead.
The completed rule is:
To get the curved length of a semicircle you divide the full circumference by 2 and for a quarter circle you divide it by 4 instead.
Work out the whole circle's circumference first, then take the fraction of it that you need.
A shape is made from a quarter circle and two straight sides. What makes up its perimeter?
The curved part plus both straight sides.
The curved part is a quarter of the full circumference, and the two straight edges are added on to it, since they are just as much part of the outline.
True or False?
Two equal semicircles in one shape have the same total curved length as one full circle.
True.
Halving the circumference and then doubling it brings you back to the whole circumference.
So you can work out the full circle once and skip the halving altogether, which saves a step and a rounding decision.
Complete the two area formulae that are not given to you:
$rectangle A = b \times______, triangle A = \frac{1}{______} \times b \times h$
The completed formulae are:
$rectangle A = b \times h, triangle A = \frac{1}{2} \times b \times h$
A triangle is half of the rectangle that would enclose it, which is where the half comes from.
True or False?
The height used to find the area of a triangle must be the length of one of its sides.
False.
It is the perpendicular height, measured at right angles to the base.
In many triangles no side runs at right angles to the base, so the height has to be worked out rather than read off the diagram.
You are given the diameter of a circle and need its area. What must you do first?
Halve the diameter to get the radius.
The given formula is $A = π r^{2}$ , which uses the radius, so putting the diameter in instead would make the answer four times too big.
A circle has a diameter of 8 cm. What is its area?
The area is 50.3 cm² to one decimal place.
Halving the diameter gives a radius of 4 cm, and $π \times 4^{2} = 50.265 . . .$
An isosceles triangle has a base of 10 cm and two equal sides of 13 cm. What is its area?
The area is 60 cm².
Splitting the triangle down the middle gives a right-angled triangle with hypotenuse 13 and base 5, so Pythagoras gives a perpendicular height of $\sqrt{13^{2} - 5^{2}} = 12$ .
Then $\frac{1}{2} \times 10 \times 12 = 60$ .
What units does an area have?
Square units, such as cm² or m².
Two lengths have been multiplied together to reach it, which is what the small 2 is recording, and leaving it off turns an area into a length.
Define composite shape.
A composite shape is one that is not a standard shape in its own right, but can be split into standard shapes.
The pieces are usually rectangles, triangles and parts of circles, all of which have area formulae you can use.
How do you find the area of a composite shape?
Split it into standard shapes and work out the area of each one separately.
Those separate areas are then combined into a single total, which is the only step where the arrangement of the pieces matters.
Complete the rule for combining the pieces:
You $______$ the areas when one shape is joined onto another, and you $______$ when one shape has been removed from another.
The completed rule is:
You add the areas when one shape is joined onto another, and you subtract when one shape has been removed from another.
Look at the diagram to see which is happening: a bite taken out of a shape is a subtraction, an extra piece stuck on is an addition.
How do you find the area of a semicircle or a quarter circle?
Work out the area of the whole circle first, using the radius.
Then divide that area by 2 for a semicircle, or by 4 for a quarter circle.
A semicircular garden of diameter 7 m has a triangle inside it, with the diameter as its base and its apex on the curved edge. What area lies outside the triangle?
The area outside the triangle is 6.99 m².
The radius is 3.5 m, so the semicircle is half of $π \times 3 . 5^{2}$ , which is 19.24 m².
The apex sits at the top of the arc, so the triangle's perpendicular height is the radius: $\frac{1}{2} \times 7 \times 3.5 = 12.25$ , and $19.24 - 12.25 = 6.99$ .
True or False?
There is only one correct way to split a composite shape into standard shapes.
False.
There is usually more than one, and every split that covers the shape exactly gives the same total area.
So it is worth pausing to pick the split that produces the easiest shapes to work with.

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