6 — Triangle Areas

Triangle Areas

Solution & Explanation · ID: A87F01A6

Question

A triangular sail has an area of 63 square feet and a base of 9 feet. Find the height of the sail.

Hint

Work backwards from the area formula to find the height. Remember that ½ × 9 = 4.5.

Concept

When we know the area and base of a triangle, we can find the height by rearranging the formula. Since A = ½ × b × h, we can solve for h = 2A ÷ b.

Show Answer

14 feet

Show Solution
1

Identify what we know: Area = 63 square feet, base = 9 feet

2

Set up the area formula: 63 = ½ × 9 × height

3

Simplify: 63 = 4.5 × height

4

Solve for height: height = 63 ÷ 4.5 = 14 feet

A triangular sail with base labeled '9 ft' along the bottom edge. A dashed vertical line shows the height labeled 'h = 14 ft' perpendicular to the base. Inside the triangle is written 'Area = 63 sq ft'. The sail has curved lines to show wind. The equation 63 = ½ × 9 × h is shown, simplified to 63 = 4.5h, then solved as h = 63 ÷ 4.5 = 14.