Unit 5 Geometry Prep Studio

A visual, interactive review for area, missing dimensions, regular polygons, volume comparisons, nets, and surface area.

Area formulas Work backward Real-world reasoning Nets and surface area Practice test
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Map

What you need to be ready for

Test skill map

The assessment is mostly about choosing the right formula, using the correct measurements, and explaining the 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 first, then decide how many items or how much money is needed.
3D figures: use volume or surface area depending on what the question asks.
Nets: add all faces, and do not confuse slant height with side length.

How to answer every problem

Circle the question. Are you finding area, height, volume, surface area, or better buy?
Choose the formula. Match the shape first. Do not start multiplying until you know the formula.
Substitute numbers. Put the given measurements in the formula.
Solve and label. Area uses square units. Volume uses cubic units. Length uses regular units.

Vocabulary snapshot

baseheight Height The straight up-and-down distance to the base. It makes a right angle.
Net A flat picture of every face of a 3D figure.
Surface area The total area covering the outside faces.
Volume The space inside a 3D figure. Use cubic units.
Lab 1

Area formula lab

Formula wall

Use the shape to pick the formula. The base and height must 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 make a right angle with the base.

Live area machine

Move the sliders. The figure updates with the side lengths, height, and second base when needed.

60 square 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 extra quick checks

Rhombus floor tile

A rhombus has base 11 cm and height 6 cm. What is the area?

Triangle banner

A triangle has base 22 ft and height 5 ft. What is the area?

Trapezoid tabletop

A trapezoid has bases 12 in. and 20 in. and height 4 in. What is the area?

Lab 2

Missing dimensions: work backward

Backward strategy

When the question gives the area and asks for a missing height or base, do not guess. Undo the formula.

Write the correct area formula.
Substitute the numbers you know.
Use inverse operations to solve for the missing measurement.
Label the answer with regular units, not square units.

Missing-dimension mini charts

Start with the original area formula. Then use the new formula that matches the missing measurement.

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 warning: missing height/base is a length, so the answer is cm, m, ft, or in. It is not cm².

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
↩Backward level-up: solve for the missing measurement

Missing rhombus base

A rhombus has area 96 cm² and height 8 cm. Find the base.

Missing triangle base

A triangle has area 45 m² and height 9 m. Find the base.

Missing trapezoid height

A trapezoid has area 105 ft² and bases 12 ft and 18 ft. Find the height.

Lab 3

Real-world geometry problems

Sod, paint, fabric, or stickers?

Real-world problems usually have two jobs: find the geometry amount, then use it to make a decision.

Geometry first: area, surface area, or volume?
Then the real world: divide by coverage, multiply by price, or compare values.
Round only when needed: if you buy whole rolls or boxes, round up.

Triangle lawn challenge

18 ft 7 ft

Each roll of sod covers 9 ft² and costs $11. Which statements are true?

Regular octagon sign

side = 8 in. a = 9.7 in.

A regular octagon has 8 equal sides. Find the approximate area.

Better buy: volume per dollar

For boxes, first find volume. Then compare how many cubic inches you get for each dollar.

BoxLengthWidthHeightPrice
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: area first, decision second

Fabric flag

A triangular flag has base 16 in. and height 9 in. Fabric costs $2 for every 12 in². What is the cost?

Painted trapezoid wall

A trapezoid wall has bases 9 ft and 15 ft and height 8 ft. One can covers 30 ft². Choose all true statements.

Snack-box value

Box A has volume 90 in³ and costs $9. Box B has volume 132 in³ and costs $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 surface area.

Square pyramid net

side = 10 m slant h = 7 m

What is the total surface area?

Net detective

Which calculation matches a square pyramid with side length 12 m and slant height 8 m?

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 bottom.

▣Nets level-up: count every outside face

Rectangular prism wrap

A box measures 6 cm by 3 cm by 4 cm. What is the surface area?

Pyramid sides only

A square pyramid has side 8 ft and slant height 11 ft. Find the lateral area only.

Pyramid total area

A square pyramid has side 5 m and slant height 6 m. Find the total surface area.

Game

Review game: formula flip + quick battle

Formula flip cards

Click each card. Say the formula before flipping.

Parallelogram
A = b × h
Triangle
A = ½ × b × h
Trapezoid
A = ½(b₁+b₂)h
Rectangular Prism SA
2lw + 2lh + 2wh

Quick battle

Solve one at a time. Get 5 correct to finish the battle.

Press Start Battle.
Boss Level

Mistake fixer

Pick the best fix for each common mistake before the final practice test.

Mistake 1

Student work: Triangle area = 18 × 7 = 126 ft².

Mistake 2

Student work: Surface area of a 4 × 5 × 8 prism = 160 cm³.

Final

Practice test

Directions

Answer each question, then press Check this question. If it is not correct yet, the page gives a hint instead of the answer so students can try again.

12 questionsTry + hint + retryAnswers hidden until checked

After the practice test

Review any missed explanations. Then redo only the tabs connected to the missed skills.

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.