Example

Finding the Height of a Triangle Given Its Area and Base

Apply the geometry problem-solving strategy to find the height of a triangle when its area and base are known.

Problem: The area of a triangular painting is 126126 square inches. The base is 1818 inches. What is the height?

  1. Read: Determine that the problem involves a triangle with an area of 126126 square inches and a base of 1818 inches. Draw and label the figure.
  2. Identify: The height of the triangle.
  3. Name: Let h=h = the height. (See the accompanying figure for the labeled area and base.)
  4. Translate: Write the triangle area formula and substitute the known values: A=12bhA = \frac{1}{2}bh 126=1218h126 = \frac{1}{2} \cdot 18 \cdot h
  5. Solve: Simplify the right side: 126=9h126 = 9h. Divide both sides by 99: 14=h14 = h.
  6. Check: Verify that an area of 126126 results from a base of 1818 and height of 1414: 121814=914=126\frac{1}{2} \cdot 18 \cdot 14 = 9 \cdot 14 = 126 \checkmark
  7. Answer: The height of the triangle is 1414 inches.
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Updated 2026-05-02

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