Math Problem Statement

How to calculate the area of an L-shaped figure with given dimensions: 22 m, 13 m, 17 m, and 23 m?

Solution

The image you uploaded shows an irregular L-shaped figure with the following dimensions:

  • Top horizontal length: 22 meters
  • Bottom horizontal length: 13 meters
  • Left vertical length: 17 meters
  • Right vertical length: 23 meters

To calculate the area of this L-shaped figure, you can divide it into two rectangles. Let's break it down step by step:

Step 1: Divide the L-shape into two rectangles

  1. Rectangle 1 (Upper part):

    • Length = 22 meters
    • Width = 13 meters
  2. Rectangle 2 (Lower part):

    • Length = (23 meters - 13 meters) = 10 meters
    • Width = 17 meters

Step 2: Calculate the area of each rectangle

  1. Area of Rectangle 1: Area1=22×13=286 square meters\text{Area}_1 = 22 \times 13 = 286 \text{ square meters}

  2. Area of Rectangle 2: Area2=17×10=170 square meters\text{Area}_2 = 17 \times 10 = 170 \text{ square meters}

Step 3: Add the areas together

The total area of the L-shaped figure is the sum of the two rectangular areas: Total Area=286+170=456 square meters\text{Total Area} = 286 + 170 = 456 \text{ square meters}

So, the area of the L-shaped figure is 456 square meters.

Would you like more details or have any questions?

Related Questions:

  1. How would you find the perimeter of this L-shaped figure?
  2. Can the area be calculated using another method?
  3. How would you calculate the area if the L-shape had curves instead of straight lines?
  4. How does breaking complex shapes into simpler ones help in finding areas?
  5. What would be the effect on the area if one of the dimensions was doubled?

Tip:

When calculating the area of irregular shapes, breaking them down into simpler shapes (like rectangles, triangles, etc.) makes the process easier and more manageable.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Decomposition of Shapes

Formulas

Area of a Rectangle = length × width

Theorems

Decomposition Method for Area Calculation

Suitable Grade Level

Grades 6-8