Math Problem Statement

Find the area of a composite shape that includes a larger rectangle (20 inches by 15 inches) and a smaller rectangle (9 inches by 8 inches) subtracted from it.

Solution

It looks like the question asks to find the area of a composite shape based on the measurements provided in the image. Here's a breakdown of the shape, which is a rectangle with a smaller rectangle subtracted:

  1. Larger Rectangle:

    • Height = 20 inches
    • Width = 15 inches
    • Area of larger rectangle = 20in×15in=300in220 \, \text{in} \times 15 \, \text{in} = 300 \, \text{in}^2
  2. Smaller Rectangle (subtracted):

    • Height = 9 inches
    • Width = 8 inches
    • Area of smaller rectangle = 9in×8in=72in29 \, \text{in} \times 8 \, \text{in} = 72 \, \text{in}^2
  3. Net Area:

    • Subtract the area of the smaller rectangle from the larger rectangle: Net Area=300in272in2=228in2\text{Net Area} = 300 \, \text{in}^2 - 72 \, \text{in}^2 = 228 \, \text{in}^2

The total area of the remaining part of the shape is 228in2228 \, \text{in}^2.

Would you like any additional details or have any questions?

Follow-up Questions:

  1. How can you break down composite shapes to calculate areas easily?
  2. Why is it necessary to subtract the area of the smaller rectangle?
  3. How would the area change if the smaller rectangle's dimensions were doubled?
  4. What are some real-life examples where this type of area calculation is useful?
  5. Could you use a similar approach to find the perimeter of this shape?

Tip:

When working with composite figures, always identify each distinct shape and calculate their areas separately before adding or subtracting as needed.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Area of Composite Shapes

Formulas

Area of a rectangle = height × width
Area of composite shape = Area of larger shape - Area of smaller shape

Theorems

Subtraction of areas in composite shapes

Suitable Grade Level

Grades 5-7