Math Problem Statement

Calculate the shaded area of a triangle divided into two smaller triangles, with the large triangle having a base of 20 meters and a height of 10 meters, and the smaller triangle on top having a base of 6 meters and an estimated height of 3 meters.

Solution

The uploaded image shows a triangle divided into two smaller triangles, with the following dimensions provided:

  • The base of the large triangle is 20 meters (10 m + 10 m on either side).
  • The height from the base to the top of the triangle is 10 meters.
  • There is a smaller triangle on top with a base of 6 meters.

To find the area of the shaded region (assuming it's the larger triangle minus the smaller triangle), here are the steps:

  1. Calculate the area of the large triangle: Area=12×base×height=12×20×10=100 square meters\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \times 10 = 100 \text{ square meters}

  2. Calculate the area of the smaller triangle: Area=12×base×height=12×6×3=9 square meters\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 3 = 9 \text{ square meters} (assuming the height of the smaller triangle is 3 meters based on visual approximation)

  3. Subtract the area of the smaller triangle from the area of the larger triangle: Shaded Area=1009=91 square meters\text{Shaded Area} = 100 - 9 = 91 \text{ square meters}

Would you like a more detailed explanation or have any questions?

Here are five related questions for further exploration:

  1. How do you calculate the height of a smaller triangle if not provided directly?
  2. What if the smaller triangle was not shaded, how would the calculation change?
  3. How can the Pythagorean theorem be used to find unknown sides in similar problems?
  4. What other methods can be used to find the area of irregular shapes?
  5. How would the calculation differ if the triangles were not right triangles?

Tip: Always double-check that all necessary dimensions are correctly interpreted from a diagram before starting calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Triangles
Subtraction of Areas

Formulas

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

Theorems

Basic Triangle Area Theorem

Suitable Grade Level

Grades 6-8