Learning Goal: Find the area of triangles, special quadrilaterals, and composite shapes by using formulas and breaking shapes into pieces.
Vocabulary
areaThe amount of flat space inside a 2D shape, measured in square units (like square feet, ft²).
baseA side of a shape you measure from. The height is measured straight up (perpendicular) from the base.
heightThe straight-line distance from the base to the top, making a square corner (90°) with the base.
composite figureA shape made of two or more simple shapes (like a rectangle plus a triangle) joined together.
decomposeTo break a shape apart into smaller, simpler shapes that are easier to measure.
What You Need to Know
Area of a triangle = 1/2 × base × height. Always use the height that makes a square corner with the base.
Area of a parallelogram = base × height (not the slanted side length).
Area of a trapezoid = 1/2 × (base₁ + base₂) × height, where the two bases are the parallel sides.
For a composite figure, decompose it into rectangles and triangles, find each area, then add them together.
The height is always perpendicular (square corner) to the base, even if drawn inside or outside the shape.
Area is always written in square units, such as cm², in², or m².
Worked Example I Do — watch how it works
A triangle has a base of 12 cm and a height of 5 cm. What is its area?
Step 1. Write the formula: Area = 1/2 × base × height.
Step 2. Put in the numbers: Area = 1/2 × 12 × 5.
Step 3. Multiply 12 × 5 = 60, then take half: 1/2 × 60 = 30.
Answer: 30 cm²
Guided Practice We Do — try it together
1. A parallelogram has a base of 9 in and a height of 6 in. Find the area.
💡 Hint: For a parallelogram, multiply base × height. Do not use the slanted side.
2. A trapezoid has parallel sides (bases) of 10 m and 6 m, and a height of 4 m. Find the area.
💡 Hint: Add the two bases first, then use 1/2 × (sum) × height.
3. A composite figure is a rectangle 8 ft long and 5 ft tall, with a triangle on top with a base of 8 ft and a height of 3 ft. Find the total area.
💡 Hint: Find the rectangle area and the triangle area separately, then add.
Independent Practice You Do — show your work
1. A triangle has a base of 14 cm and a height of 9 cm. Find the area.
2. A parallelogram has a base of 11 m and a height of 7 m. Find the area.
3. A trapezoid has bases of 12 in and 8 in and a height of 5 in. Find the area.
4. A triangle has a base of 7 ft and a height of 6 ft. Find the area.
5. A composite figure is a 10 cm by 4 cm rectangle with a triangle on one short end; the triangle has a base of 4 cm and a height of 6 cm. Find the total area.
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.G.A.1.
Item 1Selected Response6.G.A.1
A triangle has a base of 16 in and a height of 5 in. What is its area?
Select the correct answer.
Item 2Selected Response6.G.A.1
A trapezoid has parallel bases of 9 cm and 5 cm and a height of 6 cm. What is its area?
Select the correct answer.
Item 3Constructed Response6.G.A.1
A garden is a 12 m by 5 m rectangle with a triangle attached to one 12 m side. The triangle has a base of 12 m and a height of 4 m. What is the total area?
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
63 cm²
Independent 2
77 m²
Independent 3
50 in²
Independent 4
21 ft²
Independent 5
52 cm²
Item 1 · 6.G.A.1
B — Area = 1/2 × 16 × 5 = 1/2 × 80 = 40 in².
Item 2 · 6.G.A.1
A — Area = 1/2 × (9 + 5) × 6 = 1/2 × 14 × 6 = 42 cm².
Item 3 · 6.G.A.1
84 m² — Rectangle = 60 m²; triangle = 1/2 × 12 × 4 = 24 m²; total = 84 m².
Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.G.A.1