Math Problem Statement

please calculate above

Please calculate the total area of the shape shown in the image.

Solution

The image depicts a composite shape with multiple dimensions. To calculate the area, I'll break the figure into simpler rectangles and then sum their areas. Here's the calculation:


Step 1: Divide the Shape

  1. Top rectangle: 50 m × 200 m.
  2. Bottom left rectangle: 20 m × 10 m.
  3. Bottom middle rectangle: 30 m × 170 m.
  4. Right rectangle: 40 m × 400 m.

Step 2: Calculate the Area of Each Rectangle

  1. Top rectangle:
    Area=50×200=10,000m2\text{Area} = 50 \times 200 = 10,000 \, \text{m}^2

  2. Bottom left rectangle:
    Area=20×10=200m2\text{Area} = 20 \times 10 = 200 \, \text{m}^2

  3. Bottom middle rectangle:
    Area=30×170=5,100m2\text{Area} = 30 \times 170 = 5,100 \, \text{m}^2

  4. Right rectangle:
    Area=40×400=16,000m2\text{Area} = 40 \times 400 = 16,000 \, \text{m}^2


Step 3: Total Area

Total Area=10,000+200+5,100+16,000=31,300m2\text{Total Area} = 10,000 + 200 + 5,100 + 16,000 = 31,300 \, \text{m}^2


The total area of the shape is 31,300 square meters.

Would you like detailed illustrations or additional clarifications?


5 Related Questions:

  1. How can we calculate the perimeter of this shape?
  2. What if we added a boundary around the figure—how much area would that include?
  3. Can this area be divided into more symmetrical shapes for simplicity?
  4. How does the calculation change if dimensions are scaled (e.g., doubled)?
  5. Could this area fit a rectangular field of equal size?

Tip: Always double-check the alignment of dimensions when breaking composite shapes into smaller parts. Misaligned lengths can lead to errors.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Area calculation
Composite shapes
Rectangular geometry

Formulas

Area of a rectangle = length × width

Theorems

Additive property of areas for composite shapes

Suitable Grade Level

Grades 6-8