Area and Perimeter, Dimensions and Volume - Learn perimeter, area and volume for 2-D and 3-D shapes

Sep 18, 2026

Uploaded by Fahsai

Understanding perimeter, area, and volume and how they relate to the dimensions of 2-D and 3-D shapes. Covers finding perimeters by adding side lengths and converting between length units. Explains circle circumference and area using C = πd and A = πr², plus metric unit conversion. Includes surface area calculations using nets, plus volume formulas for cuboids, prisms, and cylinders. Guides checking units and deciding whether formulas represent L, L², or L³.

LanguageEnglish

CategoryExam

FormatPDF

Pages2

Reading Time5 min

AccessFree to download

Perimeter

Calculating perimeter and missing sides

Converting length units

Area

Circle circumference and area (C = πd, A = πr²)

Area of rectangles and metric units

Surface area of 3-D shapes

Volume

Volume of cuboids and prisms

Volume of cylinders

Converting volume units

Dimensions and formulas

Identifying L, L² and L³ formulas

Preventing mixed-dimension errors

Area and perimeter, dimensions and volume Understanding the difference between perimeter, area and volume. Calculating the perimeter, area and volume of different 2-D and 3-D shapes . Perimeter This measures the distance around the outline of a shape. 9 m | 5·5 m | Find the length of 9 – 6·2 = 2·8 m | | --- | --- | | | 6·2 m 13 m | | | | any missing sides. 13 – 5·5 = 7·5 m Add the lengths of the sides. 9 + 5·5 + 2·8 + 7·5 + 6·2 + 13 = 44 m Perimeter is measured in units as mm, cm, m... Converting between measurements of length ÷10 ÷100 ÷1000 mm cm m km × 10 × 100 × 1000 Area Circumference of a circle The perimeter of a circle is called the circumference. Using C to represent circumference, and d to represent diameter, we write the formula for the circumference of acircle as: C = πd Since the diameter is twice as long asthe radius (d = 2r), we can also write the formula for the circumference: C = 2πr We can use π in our calculators, or we can use an estimate of 3∙14. Area of a Circle Using A to represent area and r to represent radius, the formula for the area of a circle is: A = πr2 10cm C = 2πr = 2 × 3∙14 × 10 = 62∙8cm A = πr2 = 3∙14 × 102 = 3∙14cm2 Area This measures the amount of space within a 2-D shape. Area of a Rectangle Check that you can: • recognize 2-D shapes and their properties • recognize 3-D shapes and their properties • draw nets of 3-D shapes • substitute values into a formula • understand the relationship between units of the metric system. REMEMBER! Don’t forget to use the information you are given to calculate the lengths of any missing sides. Area and perimeter, dimensions and volume Understanding the difference between perimeter, area and volume. Calculating the perimeter, area and volume of different 2-D and 3-D shapes . Check that you can: • calculate the area of different 2-D shapes. Surface Area This is the total area of every surface (face) of a 3-D shape. It is useful to consider the net of the 3-D shape, to find the area of each face, in order to calculate the total surface area. 7 m | 5 m | C | 3 m | | | --- | --- | --- | --- | | A | B | A | B | | 5 m | C | | | 3 m 7 m Area of A = 7 × 5 = 35 m2 Area of B = 7 × 3 = 21 m2 Area ofC = 3 × 5 = 15 m2 Total surface area = 2 × (35 + 21 + 15)= 142 m2 REMEMBER! • Take care to include every side of the shape when calculating surface area. • Draw a sketch of the sides you are using for your calculation, and draw on the dimensions you need. Volume This measures the amount of space within a 3D shape. Volume of a Cuboid Volume of a cuboid = length × width × height = 8 × 5 × 3 = 120 cm2 Volume of a Prism 8cm Volume of a prism = area of the cross-section × length = 200 × 57 = 11400 mm3 Volume of a Cylinder 5cm 57mm Area = 200mm2 Volume of a cylinder = area of the cross-section × length = πr2 × l = 3∙14 × 22 × 5 = 62∙8 cm2 2cm 5cm Volume is measured in [units](units3 e.g. mm3)[3](units3 e.g. mm3)[ e.g. mm](units3 e.g. mm3)[3](units3 e.g. mm3), cm3, m3 ... Converting between measurements of volume E. g. Convert 5∙5 mm3 to cm3. 5∙5 × 100³ = 5∙5 × 1 000 000 = 5 500 000 cm3 mm3 ÷103 × 103 cm3 ÷1003 ÷10003 m3 km3 × 1003 × 10003 Remember to check the measurements are in the same units before adding or multiplying to find perimeter, area or volume. Dimensions and formulae We can decide if a formula is for a perimeter, area or volume by looking at the dimensions involved. We know that: • perimeter is a measurement of length (L): 1 dimension • area is given by a length × length (L2): 2 dimensions • volume is given by a length × length × length (L3): 3 dimensions. Deciding if a formula is length, area or volume formula Example 1: Perimeter of a rectangle = 2 × length + 2 × width = 2l + 2w Remember, numbers have no dimension. So, the expression 2l + 2w is simply a length and has one di

FAQs

What is perimeter and how is it calculated for 2-D shapes?

Perimeter measures the distance around the outline. It is found by adding the lengths of the sides, including any missing sides using the given information.

How do you calculate the area of a circle?

Use A = πr², where r is the radius. Substitute the radius value and compute the result using π (or an estimate like 3·14).

How can you tell whether a formula gives length, area, or volume?

Count the dimensions involved: perimeter is L (one length), area is L² (two lengths multiplied), and volume is L³ (three lengths multiplied). Never mix dimensions in a single calculation.

Sep 18, 2026

Uploaded by Fahsai