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

Lesson 5.25.2 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

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. measured in cm², in², ft²
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 = ½ × b × h means Area equals one-half times base times height; for b = 12 and h = 8, A = 48

How it worksWorked examplefinding the area of a triangle

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

A triangle has a base of 16 cm and a perpendicular height of 9 cm. Find the area.

  1. Two copies of a triangle form a parallelogram, so a triangle is half of one.
  2. Write the formula. A = ½ × b × h
  3. Name the parts. b = 16 cm h = 9 cm, meeting the base at a square corner
  4. Multiply, then halve. 16 × 9 = 144, and half of 144 is 72

Answer: The area of the triangle is 72 square centimeters (72 cm²).

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 a base of 14 in. and a perpendicular height of 7 in. Find the area.

  1. A triangle is half of what shape?
  2. Write the formula. A = ½ × ×
  3. Base = in. Perpendicular height = in.
  4. Multiply, then halve. × = , half is
Answer:area of the triangle

Say it and write itSentence starters

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

  • The base of the triangle is and the height is .
  • I know that measure is the height because .
  • Two copies of this triangle would compose a .
  • Area = ½ × × = square units.

Word bank triangleparallelogramhalfbaseheightperpendicularsquare cornerareaformularight trianglecopyrotate

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 5.25.2 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    6 cm7 cm10 cm
    The dashed height falls outside the triangle.

    A triangle has a base of 7 cm. Its height is 6 cm, measured outside the triangle. One slanted side is 10 cm. Find the area.

    1. 1Which length is the height: 6 cm or 10 cm?
    2. 2Multiply the base by the height.
    3. 3Take half. What is the area?
    Final answer:
  2. 2Complete each step, then write the final answer.
    45 in²h = ?10 in

    A triangle has an area of 45 square inches. Its base is 10 inches. What is its height?

    1. 1Double the area. What do you get?
    2. 2Divide by the base. What is the height?
    3. 3Why do we double the area first?
    Final answer:
  3. 3Complete 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:
  4. 4Circle the letter of the best answer. Show how you know.

    Triangle A has a base of 12 ft and a height of 4 ft. Triangle B has a base of 6 ft and a height of 8 ft. Which triangle has more area?

    1. ATriangle A
    2. BTriangle B
    3. CThey have the same area
    Show your work
  5. 5Complete each step, then write the final answer.

    A triangle-shaped flag has an area of 60 square inches. Its base is 15 inches. How tall is the flag?

    Show your work
    Final answer:
  6. 6Complete 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:

Explain your thinkingSometimes the height of a triangle falls outside the triangle. How do you find it, and why is it still the height?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help