Math Problem Statement

What is the area of this figure?

Solution

To find the area of the figure, we can break it down into simpler shapes like rectangles and potentially circles if any of those are part of the figure.

Steps:

  1. Identify the dimensions:

    • The large rectangle at the bottom: 28 yd x 8 yd.
    • The middle rectangle: 14 yd x 8 yd.
    • The two smaller rectangles on the sides: 8 yd x 6 yd each.
    • The two topmost rectangular portions: 8 yd x 8 yd each.
  2. Calculate the area of each shape:

    • Large rectangle (bottom):
      Area = 28 yd × 8 yd = 224 yd²
    • Middle rectangle:
      Area = 14 yd × 8 yd = 112 yd²
    • Two smaller rectangles on the sides:
      Area = 2 × (8 yd × 6 yd) = 96 yd²
    • Two topmost rectangles:
      Area = 2 × (8 yd × 8 yd) = 128 yd²
  3. Add up all the areas: Total Area = 224 yd² + 112 yd² + 96 yd² + 128 yd²

Let's calculate that. Areas of the different sections area_large_rectangle = 28 * 8 # 28 yd x 8 yd area_middle_rectangle = 14 * 8 # 14 yd x 8 yd area_side_rectangles = 2 * (8 * 6) # 2 * (8 yd x 6 yd) area_top_rectangles = 2 * (8 * 8) # 2 * (8 yd x 8 yd)

Total area

total_area = area_large_rectangle + area_middle_rectangle + area_side_rectangles + area_top_rectangles total_areaThe total area of the figure is 560 square yards.

Would you like further clarification or have any additional questions?

Here are some related questions you might find interesting:

  1. How would the area change if the dimensions of one of the smaller rectangles were different?
  2. What is the perimeter of this figure?
  3. How can the area of irregular shapes be calculated in a more complex figure?
  4. Can this shape be classified as a polygon? Why or why not?
  5. How would you find the area if part of the figure were a circle?

Tip: Always break down complex shapes into simpler parts to make calculations easier!

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Math Problem Analysis

Mathematical Concepts

Area
Geometry
Rectangles

Formulas

Area of a rectangle = length × width

Theorems

Addition of areas of multiple shapes

Suitable Grade Level

Grades 6-8