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Map

What you need to be ready for

Test skill map

The assessment focuses on choosing the right formula, using correct measurements, and showing all steps clearly.

Area of 2D shapes: parallelogram, rhombus, triangle, trapezoid.
Missing measurements: use the area and one dimension to solve for height or base.
Real-world area: find area, then make a practical decision (how many rolls, total cost).
3D figures: volume asks about inside space; surface area asks about outside faces.
Nets: add all faces — do not confuse slant height with side length.

Answer every problem in 4 steps

Circle the question. Area? Height? Volume? Surface area? Better buy?
Choose the formula. Match the shape first — then start substituting.
Substitute. Replace each variable with the given measurement.
Solve and label. Area → square units. Volume → cubic units. Lengths → regular units.

Vocabulary snapshot — click to test yourself

Each card shows the term. Think of the meaning, then click to reveal.

base height Height click to reveal ↓
Net click to reveal ↓
Surface Area click to reveal ↓
Volume click to reveal ↓
Lab 1

Area formula lab

Formula wall

Pick the shape, then apply the right formula. The base and height must always be perpendicular.

Parallelogram / Rhombus: A = b × h
Triangle: A = ½ × b × h
Trapezoid: A = ½ × (b₁ + b₂) × h
Common mistake: using the slanted side as the height. Height must be the straight vertical distance — it makes a right angle with the base.

Live area machine

Drag the sliders — the shape and formula update live.

60 sq units
A = 10 × 6 = 60

Visual 1 — parallelogram

b = 14 m h = 9 m

What is the area?

Visual 2 — triangle

b = 18 ft h = 8 ft

What is the area?

Visual 3 — trapezoid

b₁ = 10 b₂ = 22 h = 7

What is the area?

★Area level-up: 3 quick drills

Rhombus floor tile

A rhombus has base 11 cm and height 6 cm. Area?

Triangle banner

A triangle: base 22 ft, height 5 ft. Area?

Trapezoid tabletop

Trapezoid: bases 12 in. and 20 in., height 4 in. Area?

Lab 2

Missing dimensions — work backward

Backward strategy

When the area is given and you need a missing height or base, undo the formula step by step.

Write the correct area formula for the shape.
Substitute the numbers you already know.
Use inverse operations to isolate the missing measurement.
Label with regular units (cm, m, ft) — not square units.

Rearranged formulas — use these as a reference

Parallelogram or rhombus
OriginalA = b × h
Find heighth = A ÷ b
Find baseb = A ÷ h
Triangle
OriginalA = ½ × b × h
Find heighth = (2 × A) ÷ b
Find baseb = (2 × A) ÷ h
Trapezoid
OriginalA = ½ × (b₁ + b₂) × h
Find heighth = (2 × A) ÷ (b₁ + b₂)
Unit check: a missing height or base is a length — the answer is cm, ft, m, or in., never cm² or ft².

Checkpoint A

b = 14 m A = 210 m² h = ?

Checkpoint B

b = 14 in. A = 84 in² h = ?

Checkpoint C

b₁ = 18 cm b₂ = 24 cm A = 252 cm² h = ?
↩Backward level-up: 3 more missing-value problems

Missing rhombus base

A rhombus: area 96 cm², height 8 cm. Find the base.

Missing triangle base

A triangle: area 45 m², height 9 m. Find the base.

Missing trapezoid height

A trapezoid: area 105 ft², bases 12 ft and 18 ft. Find height.

Lab 3

Real-world geometry problems

Two-step process

Geometry first. Find the area, surface area, or volume.
Then the real world. Divide by coverage, multiply by price, or compare ratios.
Round up when buying. You can't buy a fraction of a roll or can.

Triangle lawn challenge

18 ft 7 ft

Each sod roll covers 9 ft² and costs $11. Select all true statements.

Regular octagon sign

side = 8 in. a = 9.7 in.

Find the approximate area of the octagon.

Hint: Area of regular polygon = ½ × perimeter × apothem.

Better buy: volume per dollar

Find each volume, then calculate cubic inches per dollar to compare.

BoxLWHPrice
Small4 in.6 in.3 in.$7.20
Large5 in.8 in.4 in.$12.00

Which box is the better buy?

$Real-world level-up

Fabric flag

Triangle: base 16 in., height 9 in. Fabric costs $2 per 12 in². What is the total cost?

Painted trapezoid wall

Wall: bases 9 ft and 15 ft, height 8 ft. One can covers 30 ft². Choose all true statements.

Snack-box value

Box A: 90 in³ for $9. Box B: 132 in³ for $11. Which gives more volume per dollar?

Lab 4

Nets and surface area

Rectangular prism surface area

SA = 2lw + 2lh + 2wh
5 cm 8 cm 4 cm

Find the total surface area.

Square pyramid net

side = 10 m slant = 7 m

What is the total surface area?

Net detective

Square pyramid: side 12 m, slant height 8 m. Which calculation is correct?

Sticker area: sides only

A square pyramid has base side 6 cm and slant height 8 cm. A sticker covers only the four triangular sides — not the base.

▣Nets level-up: count every face

Box wrap

Rectangular prism: 6 × 3 × 4 cm. Surface area?

Pyramid sides only

Square pyramid: side 8 ft, slant height 11 ft. Lateral area only?

Pyramid total area

Square pyramid: side 5 m, slant height 6 m. Total surface area?

Game

Review game: flip + battle

Formula flip cards

Think of the formula first — then click to flip and verify.

Parallelogram
tap to flip
A = b × h
Triangle
tap to flip
A = ½ × b × h
Trapezoid
tap to flip
A = ½(b₁+b₂)h
Rect. Prism SA
tap to flip
SA = 2lw + 2lh + 2wh
⚔ Quick Battle Get 5 correct to win
✓ 0 correct
❌ 0 wrong
📊 Q 0 / 7
Press Start Battle to begin. Solve each geometry problem as fast as you can.
★ Boss Level

Error fixer

Find and fix the mistake before the practice test.

Mistake 1

Triangle: A = 18 × 7 = 126 ft²

Mistake 2

SA of 4×5×8 prism = 160 cm³

Final

Practice test

Directions

Answer each question and press Check this question. If incorrect, you receive a hint — not the answer — so you can try again. Answers are only revealed when you grade the full test.

12 questions Try → hint → retry Answers hidden until graded

After the test

Review any missed problems — then redo the specific lab connected to each skill.

Answer key: 1) 12 ft · 2) 63 cm² · 3) area 90 / 6 rolls / $108 · 4) 6 ft · 5) 11 m · 6) 120 in² · 7) Large box · 8) 189 m² · 9) 184 cm² · 10) 175 in² · 11) 14 cm · 12) 132 cm²