Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.2Missing Measures in Triangles

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the area of a triangle using the formula A = ½ × base × height.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
BaseSpanish: Base Any side of a triangle can be the base. Once you pick a base, the height must be measured perpendicular (at a 90° angle) to it. b in A = ½bh
HeightSpanish: Altura The straight-up distance from the base to the top corner. h in A = ½bh
AreaSpanish: Área How much space is inside a flat shape. A in A = ½bh
PerpendicularSpanish: Perpendicular Two lines that meet to make a square corner (90 degrees). The corner of a book or a door frame — the edges meet at exactly 90°, shown by a small square symbol
Composite figureSpanish: Figura compuesta A shape made by putting two or more simple shapes together. A house shape = a rectangle (the walls) + a triangle (the roof); total area = rectangle area + triangle area
FormulaSpanish: Fórmula A math rule written with symbols. A = ½bh

How it worksWorked examplefinding a missing base from the area

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A triangle has an area of 150 cm² and a perpendicular height of 20 cm. Find the base.

  1. Substitute what you know. A = ½ × b × h → 150 = ½ × b × 20
  2. Undo the half by doubling the area. 2 × 150 = 300, so 300 = b × 20
  3. Divide by the measure you already know. 300 ÷ 20 = 15
  4. Check by working forward. ½ × 15 × 20 = 150

Answer: The base of the triangle is 15 centimeters.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A triangle has an area of 96 ft² and a perpendicular height of 16 ft. Find the base.

  1. Substitute what you know. = ½ × b ×
  2. Double the area. 2 × = , so = b ×
  3. Divide by the measure you know. ÷ =
  4. Check forward. ½ × × =
Answer:base of the triangle

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The area is and the measure I already know is .
  • I doubled the area because .
  • The missing measure is .
  • I checked by working forward: ½ × × = .

Word bank areabaseheightformulasubstitutedoubledividehalfundocheckperpendicularsquare units

Watch outA common mistake

A common mistake in Area of Triangles is forgetting the ½ — students multiply base × height like a rectangle and stop there, or they use the triangle's slanted side instead of the perpendicular height that's already given. Always check: did I take half, and did I use the straight-up height, not the slanted side?

Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.2Missing Measures in Triangles

Apply Day · Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the area of a triangle using the formula A = ½ × base × height.

  1. 1Complete each step, then write the final answer.
    3 m4 m

    A triangle has a base of 4 m and a height of 3 m. Find its area.

    Show your work

    Hint Multiply the base by the height. Then take half.

    Final answer:
  2. 2Complete each step, then write the final answer.

    A triangle has a base of 10 in and a height of 5 in. Find its area.

    Show your work

    Hint Multiply 10 × 5. Then take half.

    Final answer:
  3. 3Complete each step, then write the final answer.

    A garden is shaped like a triangle. Its base is 14 m and its height is 3 m. What is its area?

    Show your work

    Hint Multiply the base by the height. Then take half.

    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.2Missing Measures in Triangles

Apply Day · Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the area of a triangle using the formula A = ½ × base × height.

  1. 1Complete each step, then write the final answer.

    Sam says a triangle with a base of 10 in and a height of 7 in has an area of 70 square inches. Is he right? What is the area?

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    A triangle has an area of 28 square meters. Its height is 8 m. How long is its base?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    A triangle has a base of 12 cm and a height of 5 cm. Find its area.

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 5: Solve Area, Surface Area, and Volume ProblemsStandard 6.GR.1

Lesson 5.2Missing Measures in Triangles

Apply Day · ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the area of a triangle using the formula A = ½ × base × height.

  1. 1Circle the letter of the best answer. Show how you know.

    A triangular garden bed has a base of 14 meters and a perpendicular height of 6 meters. What is its area?

    1. A10 square meters
    2. B20 square meters
    3. C42 square meters
    4. D84 square meters
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 2Complete each step, then write the final answer.

    A triangle has an area of 30 square centimeters and a base of 12 cm. Kim says the height is 2.5 cm, because 30 ÷ 12 = 2.5. What is the correct height?

    Show your work
    Final answer:
  3. 3Complete each step, then write the final answer.

    A triangle has an area of 54 square feet. Its base is 12 feet. What is its height?

    Show your work
    Final answer:
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help