Math Problem Statement

Find the area of the triangle. The triangle has a base of 19 yards, a height of 7 yards, and a side length of 15 yards.

Solution

The image depicts a triangle where:

  • The base of the triangle is 19yd19 \, \text{yd},
  • The height (perpendicular from the base to the opposite vertex) is 7yd7 \, \text{yd}.

The formula to find the area AA of a triangle is:

A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}

Substituting the given values:

A=12×19yd×7ydA = \frac{1}{2} \times 19 \, \text{yd} \times 7 \, \text{yd} A=12×133yd2=66.5yd2A = \frac{1}{2} \times 133 \, \text{yd}^2 = 66.5 \, \text{yd}^2

Thus, the area of the triangle is 66.5 square yards.

Would you like further details, or do you have any questions?

Here are some related questions:

  1. How would the area change if the base was doubled?
  2. What is the perimeter of the triangle given its sides?
  3. Can you calculate the hypotenuse if this was a right triangle?
  4. How does the area formula for a triangle relate to other shapes?
  5. What if you only knew two sides and the angle between them—could you still find the area?

Tip: Always ensure the height used in the area calculation is perpendicular to the base!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Area of Triangles

Formulas

Area of a triangle: A = (1/2) × base × height

Theorems

Basic area formula for triangles

Suitable Grade Level

Grades 6-8