Unit 5 · Geometry Review Arcade

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.

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.

Shape

Result

60 sq units

Base b = 10

Height h = 6

Second base b₂ = 16

A = 10 × 6 = 60

Visual 1 — parallelogram

What is the area?

Visual 2 — triangle

What is the area?

Visual 3 — trapezoid

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

Height (in meters)

Checkpoint B

Height (in inches)

Checkpoint C

Height (in centimeters)

↩Backward level-up: 3 more missing-value problems

Missing rhombus base

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

Base (cm)

Missing triangle base

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

Base (m)

Missing trapezoid height

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

Height (ft)

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

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

The lawn area is 63 ft². The yard needs 7 rolls. The total cost is $77. The lawn area is 126 ft².

Regular octagon sign

Find the approximate area of the octagon.

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

Area (in²)

Better buy: volume per dollar

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

Box	L	W	H	Price
Small	4 in.	6 in.	3 in.	$7.20
Large	5 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.

Area is 96 ft². Painter needs 4 cans. Area is 192 ft². Painter needs exactly 3 cans.

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

Surface area formula wall

Surface area means the total area of the outside faces. Choose the formula that matches the solid.

Rectangular prism

SA = 2lw + 2lh + 2wh

Find the area of each pair of matching faces, then add them.

Square pyramid — total surface area

SA = s² + 4(½ × s × l)

Add the square base plus the four triangular faces. l means slant height.

Net strategy

SA = sum of all face areas

Use the net to count every face. Do not use volume when the question asks for outside area.

Rectangular prism surface area

SA = 2lw + 2lh + 2wh

Find the total surface area.

Square pyramid net

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.

Lateral area (cm²)

▣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?

Lateral area (ft²)

Pyramid total area

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

Arcade

Pie Mr. Neft review battle

How the pie battle works

Press Start battle to load a review problem.

Type the numerical answer only. Use formulas and units on paper if needed.

If you are correct, the pie splats on Mr. Neft's face and your hit meter goes up.

If you are wrong, the pie misses. Read the hint, then try the next one.

Teacher-approved challenge: the battle is playful, but every hint still reinforces the geometry skill behind the question.

Fast review targets

Use the right formula first: prism surface area is not volume.

For triangles, remember the one-half before multiplying.

For nets, add every face and watch the labels carefully.

For missing dimensions, undo the formula with inverse operations.

Press Start Battle to begin the pie challenge.

🎯 Hits: 0

💨 Misses: 0

🧩 Problem: 0

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. When finished, grade the full test and create a turn-in report for Google Classroom.

12 questions Try → hint → retry Answers hidden until graded

Google Classroom turn-in report

Type your name before you begin. Your practice test work autosaves on this device. As you work, the page saves your section progress on this device. Create a section-by-section report, then copy or download it and attach it in Google Classroom.

Student name

After the test

Review any missed problems, redo the specific lab connected to each skill, and submit your turn-in report in Google Classroom.