PSHS NCE Perimeter and Area Reviewer

TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Perimeter and Area

Know whether a problem is asking for the boundary or the space inside, then use the shortest correct formula.

Visual geometryGrade 6–7 friendlyPerimeter vs areaQuick Fire + Mastery

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Perimeter and Area

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Around or inside?

Perimeter = distance around the outside.
Area = amount of flat space inside.

Fast clue: fence, border, frame, edge, around → think perimeter.
floor, field, tile, cover, inside → think area.

VISUAL GUIDE

See what each formula measures

RECTANGLE

Rectangle: P = 2L + 2W, A = L × W

TRIANGLE

Triangle area: A = 1/2 × base × height

PARALLELOGRAM

Parallelogram area: A = base × perpendicular height

TRAPEZOID

Trapezoid area: A = 1/2 × (b₁ + b₂) × h

WORKED EXAMPLES

Six patterns you should recognize

1. Rectangle perimeter

Length 9 cm, width 4 cm.

2(9) + 2(4) = 26 cm

26 cm

2. Rectangle area

Length 9 cm, width 4 cm.

9 × 4 = 36 cm²

36 cm²

3. Square

A square has side 7 m.

P = 4(7) = 28 m
A = 7 × 7 = 49 m²

4. Triangle area

Base 12 cm, height 5 cm.

1/2 × 12 × 5 = 30 cm²

30 cm²

5. Parallelogram area

Base 10 m, perpendicular height 6 m.

10 × 6 = 60 m²

60 m²

6. Missing dimension

A rectangle has area 48 cm² and width 6 cm. Find the length.

48 ÷ 6 = 8 cm

8 cm

TRY WITH ME

Choose perimeter or area first

A rectangular playground is 15 m long and 8 m wide. A fence will go all the way around it.

1. Fence means around the outside.
2. So use perimeter.
3. 2(15) + 2(8) = 30 + 16.

46 m of fencing

COMMON TRAPS

Watch out for these

Using perimeter for flooring.
Flooring covers inside space, so use area.

Forgetting the 1/2 in triangle area.
A triangle is half of a matching parallelogram or rectangle.

Using the slanted side as height.
Height must be perpendicular to the base.

Wrong units.
Perimeter uses linear units. Area uses square units.

REGULAR PRACTICE

Build the skill

These mix rectangle, square, triangle, parallelogram, trapezoid, and missing-dimension problems.

QUICK FIRE

Around or inside?

Five fast questions. Identify the quantity before calculating.

Question 1 of 5

FRESH MASTERY CHECK

Can you do it without hints?

Score 5/5 to verify this competency. If you miss one, a fresh set will be ready.

NEED HELP?

Still mixing up perimeter and area?

Send Teacher Abi the exact item that confused you. I can help you identify what the problem is measuring before you calculate.

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