Secondary 2 Missing Measurements and Unit Conversion

All 10 questions

Each question targets one named concept from the sheet. Read them here, or print the PDF — it has working space under each one.

1. Q1Finding Missing Measurements in Plane Figures From the Perimeter

   Find the missing length in each figure. Show the equation you solve.

   1. A rectangular banner has a perimeter of $96\text{ cm}$ and is $18\text{ cm}$ wide. How long is it?
   2. An isosceles triangle has a perimeter of $74\text{ cm}$. Its two equal sides each measure $26\text{ cm}$. How long is the base?
   3. A rectangular hockey-card display has a perimeter of $54\text{ dm}$, and its length is twice its width. Find both dimensions.
2. Q2Finding Missing Measurements in Plane Figures from their Area

   Each figure's area is given. Find the missing measurement.

   1. A parallelogram has an area of $84{\text{ cm}}^2$ and a base of $12\text{ cm}$. Find its height.
   2. A triangle has an area of $45{\text{ cm}}^2$ and a height of $9\text{ cm}$. Find the base that goes with that height.
   3. A trapezoid has an area of $72{\text{ cm}}^2$ and parallel sides measuring $9\text{ cm}$ and $15\text{ cm}$. Find its height.
3. Q3Missing Measurements According to Area: Decomposable and Truncated Solids

   A storage bin is an open-topped rectangular prism with a base measuring $40\text{ cm}$ by $30\text{ cm}$. The inside of the base and all four walls are coated, and the coated surface measures $4000{\text{ cm}}^2$. Find the height of the bin.

4. Q4Missing Measurements in Plane Figures

   For each situation, name the measurement formula you would start from, say which letter you are solving for, and state the first step you would take — or explain why the information you are given is not enough. Do not carry out the arithmetic.

   1. You know a triangle's area and its base, and you want its height.
   2. You know a rectangle's perimeter and that it is three times as long as it is wide, and you want its width.
   3. You know a trapezoid's area, its height and one of its parallel sides, and you want the other parallel side.
   4. You know only a rectangle's perimeter, and you want its area.
5. Q5Missing Measurements of Solids from the Area

   Find the missing measurement of each solid.

   1. A cube has a total surface area of $294{\text{ cm}}^2$. Find its edge.
   2. The label on a cylindrical can covers the curved side only and has an area of $240\pi {\text{ cm}}^2$. The can's radius is $6\text{ cm}$. Find its height.
   3. A pyramid with a square base of edge $10\text{ cm}$ has a lateral area (the four triangular faces) of $260{\text{ cm}}^2$. Find the slant height of one triangular face.
6. Q6Missing Measures from a Volume: Decomposable and Truncated Solids

   A water trough is made by joining two rectangular prisms end to end. The first measures $120\text{ cm}$ long, $40\text{ cm}$ wide and $25\text{ cm}$ deep. The second is $60\text{ cm}$ long, $40\text{ cm}$ wide and $h$ cm deep. Together they hold $168000{\text{ cm}}^3$. Find $h$.

7. Q7Units for Measuring Area and Their Conversion

   Convert each measurement.

   1. $4.5{\text{ m}}^2$ into ${\text{cm}}^2$
   2. $320000{\text{ cm}}^2$ into ${\text{m}}^2$
   3. $7{\text{ dm}}^2$ into ${\text{mm}}^2$
   4. $0.6{\text{ km}}^2$ into ${\text{m}}^2$
8. Q8Units for Measuring Mass and Their Conversion

   Convert or compute.

   1. $3.2\text{ kg}$ into $\text{g}$
   2. $4500\text{ mg}$ into $\text{g}$
   3. $0.75\text{ t}$ into $\text{kg}$
   4. A camping bag holds six pouches of $850\text{ g}$ each plus a stove of $1.4\text{ kg}$. Give the total mass in kilograms.
9. Q9Units of Time and Their Conversion

   Convert or compute.

   1. $3\text{ h }25\text{ min}$ into minutes
   2. $9000\text{ s}$ into hours and minutes
   3. $1.75\text{ h}$ into minutes, then into seconds
   4. A film lasting $2\text{ h }15\text{ min}$ starts at $18:50$. At what time does it end?
10. Q10Synthesis — drawing on several sheets in this topic

    A rectangular patio is to have an area of $12{\text{ m}}^2$, and the space available makes it exactly $250\text{ cm}$ wide.

    1. Find the length of the patio in metres.
    2. Give that length in centimetres.
    3. Give the patio's area in ${\text{cm}}^2$, and check that it agrees with your two side lengths in centimetres.

The 9 challenge problems for this topic are a separate, paid sheet and are not reproduced here.

The rest of this unit

The worksheet is the practice, and it is free. Two more printable documents cover the same unit and come with the Secondary 2 Math bundle: read the notes first, work this sheet, then sit the test closed-book. See what each one covers.

What the Missing Measurements and Unit Conversion notes cover  About the Missing Measurements and Unit Conversion unit test

How to do every concept on this sheet

This is the part worksheet sites usually leave out. Below is the actual reasoning behind each group of questions — not a full solution set, the decisions that get you to one. Read it before you start, or after you get stuck.

One method, run on six kinds of figure

Q1, Q2, Q3, Q5 and Q6 are the same four steps applied to a rectangle, a triangle, a trapezoid, a cube, a cylinder, a pyramid, an open bin and a pair of joined prisms. Learning them as eight separate recipes is what makes this topic feel long. It is one recipe.

Q4 asks for the plan, not the answer

Q4 gives four situations and forbids arithmetic. Name the formula, name the letter you are solving for, state the first step — or explain why what you have been given is not enough. That last branch is the reason the question exists.

Lateral area or total area — the question the wording answers (Q5)

Q5 and its harder partner turn on one distinction. A label wrapping a can covers the curved surface only. Sheet metal for a closed can covers the curved surface and both discs. The two lead to different equations from the same numbers:

Given a cylinder's total area, a student who writes 10πh = 100π has quietly used the lateral formula on a total area. The fix is to subtract the two discs from the given total first, and only then divide. Read the object: a rain barrel open at the top has one disc, a can has two, a label has none.

Decomposable and truncated solids: subtract before you solve (Q6)

When part of the solid is already fully known, take it out of the total first and you are left with the ordinary one-unknown problem you already know how to do. Q6's trough is two prisms holding 168 000 cm³ between them: the first prism's volume is computable outright, so subtract it and the second prism's depth falls out in a single division.

A solid with a channel cut through it works the same way in reverse — start from the whole block, subtract the removed piece, and set the result equal to what is left. The only extra care it needs is the units: a volume quoted in dm³ and dimensions given in cm have to be brought to the same unit before the equation means anything, and that conversion is not the one most people expect.

Area units square the factor, volume units cube it (Q7)

This is the idea the whole conversion half rests on, and it is worth being able to justify rather than just remember. One metre is 100 cm. A square of one metre on each side is therefore 100 cm by 100 cm:

So the factor between two length units gets squared for areas and cubed for volumes. Converting an area with the plain length factor instead gives 2.4 m² = 240 cm², which is off by a factor of a hundred. Drawing that one-metre square once is the fastest way to see why, and it is worth doing on paper rather than taking on trust.

Mass, and the rounding that goes downwards (Q8)

Mass converts on plain powers of ten — milligram, gram, kilogram, tonne — and Q8 mixes a conversion into a computation: six pouches in grams plus a stove in kilograms, answered in kilograms. Convert everything to one unit before adding a single pair of numbers.

Time is not decimal (Q9)

An hour is 60 minutes, not 100, and that is the whole difficulty. Typing 2.47 + 1.55 into a calculator to add 2 h 47 min and 1 h 55 min treats minutes as hundredths of an hour and lands 40 minutes short — a single mistake that accounts for most wrong time totals.

Q10: two units in one problem

The synthesis question sets an area in square metres against a width given in centimetres, and asks for the answer both ways. Convert to a single unit before you divide — mixing metres and centimetres inside one formula produces a number that is wrong by a factor of a hundred and looks entirely reasonable.

Then do what part c) asks even when a question does not ask it: recompute the area from the two side lengths in the other unit and check that the two agree. That agreement is the whole point of the squaring rule, and it is a check you can run on any conversion you are unsure of.

Getting the most out of it

Write the formula with letters before any number appears

Every question in the first half is a formula run backwards, so the formula has to be on the page before it can be run in either direction. Write it, substitute, then solve — in that order, every time.

Decide which surfaces are actually counted

Open at the top, coated on the inside, painted except where it rests on the ground, labelled on the curved side only: each of those phrases changes the equation. Underline the phrase in the question and list the surfaces before writing anything.

Put your answer back into the question, not into your equation

Substituting into your own equation only confirms your algebra. Recomputing the perimeter, area or volume from the original wording confirms the whole solution, and it is the only check that catches a formula misremembered in the first line.

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