Geometry & Measurement

Interactive study guide — Reveal Math Unit 5 · Standard 6.G

5.1 — Area of Parallelograms

Find the area of a parallelogram using its base and perpendicular height.

Key Ideas

A parallelogram has two pairs of parallel sides. To find the area, multiply the base by the height.

Formula: A = b × h

The height must be perpendicular to the base — not the slanted side. Think of it as the straight-up distance between the base and the opposite side.

Example: A parallelogram has a base of 8 cm and a height of 5 cm.
A = 8 × 5 = 40 sq cm
Tip: You can cut a parallelogram and rearrange it into a rectangle with the same base and height — that's why the formula works!

Practice

A parallelogram has a base of 12 cm and a height of 7 cm. What is the area?

38 sq cm
84 sq cm
19 sq cm

Which measurement must be perpendicular to the base when finding area of a parallelogram?

The height
The slant side
The diagonal

A parallelogram has an area of 54 sq in and a base of 9 in. What is the height?

5 in
63 in
6 in
Score
0/3

5.2 — Area of Triangles

A triangle is half of a parallelogram, so its area formula uses one-half.

Key Ideas

Two identical triangles can always be arranged to form a parallelogram. That's why the area of a triangle is half the area of the related parallelogram.

Formula: A = ½ × b × h

The height is still the perpendicular distance from the base to the opposite vertex.

Example: A triangle has a base of 10 in and a height of 6 in.
A = ½ × 10 × 6 = ½ × 60 = 30 sq in
Tip: Multiply base × height first, then divide by 2. It's easier that way!

Practice

A triangle has a base of 14 cm and a height of 8 cm. What is the area?

112 sq cm
22 sq cm
56 sq cm

Why is the area formula for a triangle ½ × b × h?

A triangle is half of a parallelogram
A triangle has half as many sides
You always divide shapes by 2

A triangle has an area of 24 sq ft and a base of 8 ft. What is the height?

3 ft
6 ft
16 ft
Score
0/3

5.3 — Area of Trapezoids & Composite Figures

Use the trapezoid formula and break composite figures into simpler shapes.

Trapezoid Area

A trapezoid has exactly one pair of parallel sides called bases (b₁ and b₂).

Formula: A = ½(b₁ + b₂) × h

Add the two bases, multiply by the height, then take half.

Example: A trapezoid has bases of 4 and 8 units and a height of 5 units.
A = ½(4 + 8) × 5 = ½(12) × 5 = 6 × 5 = 30 sq units

Composite Figures

A composite figure is made up of two or more simple shapes. Break it apart, find each area, then add them together.

Strategy: Look for rectangles, triangles, parallelograms, or trapezoids hiding inside the composite shape. Find each area separately, then combine.

Practice

A trapezoid has bases of 6 cm and 10 cm and a height of 4 cm. What is the area?

40 sq cm
32 sq cm
24 sq cm

To find the area of a composite figure, you should:

Break it into simpler shapes and add their areas
Multiply length × width
Use only the trapezoid formula

A trapezoid has bases of 5 in and 9 in and a height of 6 in. What is the area?

30 sq in
54 sq in
42 sq in
Score
0/3

5.4–5.5 — Nets & Surface Area

Unfold 3D shapes into nets and find surface area by adding the areas of all faces.

Key Ideas

A net is a 2D pattern that folds into a 3D shape. Each face of the solid becomes a flat shape in the net.

Surface area (SA) is the total area of all the faces of a 3D figure.

Rectangular Prism

A rectangular prism has 6 faces (3 pairs of identical rectangles).

Formula: SA = 2(lw + lh + wh)

Example: A rectangular prism is 3 × 4 × 5.
SA = 2(3×4 + 3×5 + 4×5) = 2(12 + 15 + 20) = 2(47) = 94 sq units
Tip: Draw or visualize the net — it helps you see all 6 faces and avoid missing any.

Practice

A rectangular prism is 2 × 3 × 6. What is the surface area?

72 sq units
36 sq units
66 sq units

How many faces does a rectangular prism have?

4
8
6

A cube has edges of 5 cm. What is its surface area?

125 sq cm
150 sq cm
100 sq cm
Score
0/3

5.6–5.8 — Volume of Rectangular Prisms

Find the volume of rectangular prisms, including those with fractional edge lengths and composite 3D figures.

Key Ideas

Volume measures the space inside a 3D figure, in cubic units.

Formulas: V = l × w × h  or  V = B × h (where B is the area of the base)

Example: A rectangular prism is 6 × 4 × 3.
V = 6 × 4 × 3 = 72 cubic units

Fractional Edge Lengths

The same formula works with fractions. Multiply carefully.

Example: V = 2½ × 3 × 4 = 5/2 × 3 × 4 = 30 cubic units

Composite 3D Figures

Break composite solids into separate rectangular prisms, find each volume, then add them together.

Practice

A rectangular prism is 5 × 8 × 3. What is the volume?

79 cubic units
40 cubic units
120 cubic units

A rectangular prism has a base area of 20 sq cm and a height of 7 cm. What is the volume?

140 cubic cm
27 cubic cm
54 cubic cm

A rectangular prism is ½ × 4 × 6. What is the volume?

24 cubic units
12 cubic units
10 cubic units
Score
0/3

Vocabulary

Tap a card to reveal the definition.

Area
The amount of space inside a 2D shape, measured in square units.
Base
The bottom side of a shape used in area formulas. A trapezoid has two bases.
Height
The perpendicular distance from the base to the top of a shape.
Perpendicular
Meeting at a right angle (90°). The height is always perpendicular to the base.
Parallelogram
A quadrilateral with two pairs of parallel sides. Area = base × height.
Trapezoid
A quadrilateral with exactly one pair of parallel sides (the bases).
Composite Figure
A shape made up of two or more simple shapes combined together.
Net
A 2D pattern that can be folded to form a 3D solid.
Surface Area
The total area of all the faces of a 3D figure, measured in square units.
Volume
The amount of space inside a 3D figure, measured in cubic units.
Rectangular Prism
A 3D solid with 6 rectangular faces. Think of a box shape.
Cubic Units
Units used to measure volume, like cubic centimeters (cm³) or cubic inches (in³).
Face
A flat surface on a 3D solid. A rectangular prism has 6 faces.
Edge
A line segment where two faces of a 3D solid meet.
Vertex
A point where three or more edges meet on a 3D solid. Plural: vertices.