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

Lesson 5.2Determine the Area of 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.

Why This Matters Your architecture firm is designing a park with triangular garden beds. The client wants to know exactly how much soil to order, which means calculating the area of each triangular section. The first garden has a base of 12 feet and a height of 8 feet.

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 example

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

A triangle has a base of 14 cm and a height of 9 cm. Find its area.

  1. 14 × 9 = 126
  2. 126 is the parallelogram made by two triangles.
  3. 126 ÷ 2 = 63

Answer: 63 cm²

Now you trySame steps, your turn

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

Now a smaller triangle: base = 10 cm, height = 6 cm.

Answer:

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 out!A common mistake

A common mistake in Area of Triangles is forgetting the ½

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

Lesson 5.2Determine the Area of Triangles

Level 0Most support · every hint printed

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.

Why This Matters Your architecture firm is designing a park with triangular garden beds. The client wants to know exactly how much soil to order, which means calculating the area of each triangular section. The first garden has a base of 12 feet and a height of 8 feet.

How it worksWorked example

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

A triangle has a base of 14 cm and a height of 9 cm. Find its area.

  1. 14 × 9 = 126
  2. 126 is the parallelogram made by two triangles.
  3. 126 ÷ 2 = 63

Answer: 63 cm²

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

    What is the area of a triangle with base 10 cm and height 6 cm?

    1. A16 sq cm
    2. B30 sq cm
    3. C30 cm
    4. D60 sq cm
    Steps to try
    1. You have a base of 10 cm and a height of 6 cm — a triangle needs only those two, plus one special step.
    2. A triangle is half of a rectangle: use A = ½ × b × h. If you only multiply, your answer is twice too big.
    3. Multiply 10 × 6, then take half of the product. Area units are square centimeters.
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  2. 2Circle the letter of the best answer. Show how you know.

    A triangular garden bed in the firm's park design has an area of 24 sq ft and a base of 8 ft. What is the height?

    1. A3 ft
    2. B6 ft
    3. C12 ft
    4. D16 ft
    Steps to try
    1. The area (24 sq ft) and base (8 ft) are given — you're solving backwards for the height.
    2. Simplify first: ½ × 8 = 4, so the equation becomes 24 = 4 × h.
    3. Divide 24 by 4 to find the height in feet.
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  3. 3Circle the letter of the best answer. Show how you know.

    Why do we divide by 2 when finding the area of a triangle?

    1. AA triangle is exactly half of a rectangle with the same base and height
    2. BTriangles have 2 equal sides
    3. CThe base is always twice the height
    4. DWe always divide area formulas by 2
    Steps to try
    1. Think about drawing a diagonal across a rectangle — what two shapes does it create?
    2. Compare a triangle to a rectangle with the same base and height. How much of the rectangle does the triangle cover?
    3. Sketch a rectangle, draw one diagonal, and shade one triangle. What fraction of the rectangle did you shade?
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    What is the area of a triangle with base 14 ft and height 6 ft?

    1. A20 sq ft
    2. B42 sq ft
    3. C42 ft
    4. D84 sq ft
    Steps to try
    1. Base 14 ft and height 6 ft — remember what makes a triangle's area different from a rectangle's.
    2. Use A = ½ × b × h: compute the full product first, then halve it. Area needs square units.
    3. Find 14 × 6, then take half of that product. Write the units as sq ft.
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?

Explain your thinkingThe triangle fits inside a 12 × 8 rectangle. How does the triangle's area compare to the rectangle's area?

Sentence starter The area of the triangle is ___ the rectangle because A = 1/2 × ___ × ___ = ___ square feet.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help