Math Problem Statement

What is the area of this figure?

Solution

The figure shown in the image is a compound shape made up of rectangles. To find the total area, we need to break the figure into simpler rectangular sections and sum their areas.

Step-by-step breakdown:

  1. First Rectangle (Left side):

    • Dimensions: 5 m by 10 m.
    • Area = 5m×10m=50square meters5 \, \text{m} \times 10 \, \text{m} = 50 \, \text{square meters}.
  2. Second Rectangle (Top right):

    • Dimensions: 14 m by 6 m.
    • Area = 14m×6m=84square meters14 \, \text{m} \times 6 \, \text{m} = 84 \, \text{square meters}.
  3. Third Rectangle (Bottom right):

    • Dimensions: 6 m by 2 m.
    • Area = 6m×2m=12square meters6 \, \text{m} \times 2 \, \text{m} = 12 \, \text{square meters}.
  4. Fourth Rectangle (Right bottom corner):

    • Dimensions: 3 m by 2 m.
    • Area = 3m×2m=6square meters3 \, \text{m} \times 2 \, \text{m} = 6 \, \text{square meters}.

Now, sum up the areas: Total Area=50+84+12+6=152square meters\text{Total Area} = 50 + 84 + 12 + 6 = 152 \, \text{square meters}

Thus, the area of the figure is 152 square meters.

Would you like further clarification or more details? Here are a few related questions to consider:

  1. How can you find the perimeter of this compound figure?
  2. What would happen to the total area if one of the rectangles changed in size?
  3. How can you break down a compound shape into different shapes, like triangles?
  4. How do you calculate the area of a triangle, and when would you use it?
  5. How can you verify the correctness of your solution by reconstructing the figure?

Tip: Always label each part of a compound figure clearly, so it’s easier to break down into smaller shapes for calculating areas.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Area of Compound Figures
Rectangles

Formulas

Area of a rectangle = length × width

Theorems

-

Suitable Grade Level

Grades 6-8