Math Problem Statement

Determine the area of the shaded regions in a rectangle with sides RE, EC, GT, and TR. The rectangle has a base of 60 ft and a height of 20 ft. The unshaded triangle inside the rectangle has the same base and height.

Solution

The image shows a problem asking to find the area of shaded regions within a rectangle. Here's how we can solve it:

  1. Dimensions of the Rectangle:
    The rectangle has a base RE=60ftRE = 60 \, \text{ft} and height EC=20ftEC = 20 \, \text{ft}.

    The area of the rectangle is given by: Area of rectangle=base×height=60×20=1200square feet\text{Area of rectangle} = \text{base} \times \text{height} = 60 \times 20 = 1200 \, \text{square feet}

  2. Unshaded Triangle:
    The unshaded triangle is inside the rectangle with the same base and height. The base of the triangle is AC=60ftAC = 60 \, \text{ft}, and its height is also 20ft20 \, \text{ft} (since CT=20ftCT = 20 \, \text{ft}, the same as the rectangle's height).

    The area of a triangle is given by: Area of triangle=12×base×height=12×60×20=600square feet\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 60 \times 20 = 600 \, \text{square feet}

  3. Shaded Area:
    The shaded region is the area of the rectangle minus the area of the triangle: Shaded area=Area of rectangleArea of triangle=1200600=600square feet\text{Shaded area} = \text{Area of rectangle} - \text{Area of triangle} = 1200 - 600 = 600 \, \text{square feet}

Thus, the shaded region has an area of 600 square feet.

Would you like more details or have any questions?

Here are five follow-up questions to expand understanding:

  1. How do we calculate the area of any general triangle?
  2. Why do we subtract the unshaded triangle's area from the rectangle's area to find the shaded regions?
  3. Can this method be applied to different shapes besides triangles, such as circles or trapezoids?
  4. How would the calculation change if the unshaded region were not triangular?
  5. What other methods could you use to check the area of the shaded region?

Tip: When calculating areas, make sure all dimensions are in the same units before performing any operations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation

Formulas

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

Theorems

Basic Area Calculation

Suitable Grade Level

Grades 6-8