Math Problem Statement

Find the area of the triangle with a base of 16.9 ft and a height of 10.4 ft.

Solution

To find the area of a right triangle, we can use the formula:

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

From the image:

  • The base of the triangle is 16.9 feet.
  • The height of the triangle is 10.4 feet.

Now, let's calculate the area.

Area=12×16.9×10.4\text{Area} = \frac{1}{2} \times 16.9 \times 10.4

I'll compute this now.The area of the triangle is 87.88ft287.88 \, \text{ft}^2. However, the problem specifies that the exact answer is needed without rounding.

Since the base and height are given to two decimal places, the exact answer here would still be 87.88ft287.88 \, \text{ft}^2.

Would you like more details or further explanations on this?

Here are five related questions:

  1. How do you calculate the area of an equilateral triangle?
  2. What is the relationship between the base and height in isosceles triangles?
  3. How does the Pythagorean theorem relate to the area of right triangles?
  4. Can you calculate the perimeter of this triangle using the given base and height?
  5. What other methods can be used to find the area of a triangle?

Tip: Always make sure you correctly identify the base and height when solving area problems, especially for right triangles!

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Right Triangle

Formulas

Area of a Triangle = 1/2 × base × height

Theorems

Pythagorean Theorem (for right triangles)

Suitable Grade Level

Grades 6-8