Math Problem Statement

Selena took two congruent squares and a parallelogram to create a figure. The figure she created is shown below.

What is the area of the figure in square meters? A.34.8 m2 B.18 m2 C.16.8 m2 D.9 m2

Selena took two congruent squares and a parallelogram to create a figure. The figure she created is shown below. What is the area of the figure in square meters? A.34.8 m2 B.18 m2 C.16.8 m2 D.9 m2

Solution

To determine the area of the figure, we break it into its individual components: the two congruent squares and the parallelogram.

Step-by-step Calculation:

  1. Area of the two squares:

    • Each square has a side length of 3m3 \, \text{m}.
    • Area of one square = side2=32=9m2\text{side}^2 = 3^2 = 9 \, \text{m}^2.
    • Since there are two squares, their total area is: 2×9=18m2.2 \times 9 = 18 \, \text{m}^2.
  2. Area of the parallelogram:

    • The base of the parallelogram is 6m6 \, \text{m}.
    • The height of the parallelogram is 2.8m2.8 \, \text{m}.
    • Area of the parallelogram = base×height=6×2.8=16.8m2\text{base} \times \text{height} = 6 \times 2.8 = 16.8 \, \text{m}^2.
  3. Total Area of the Figure:

    • Sum the areas of the squares and the parallelogram: 18+16.8=34.8m2.18 + 16.8 = 34.8 \, \text{m}^2.

Final Answer:

The total area of the figure is 34.8m234.8 \, \text{m}^2.

Correct Option: A. 34.8m234.8 \, \text{m}^2.


Would you like additional details on this solution or related concepts?

Related Questions:

  1. How do you calculate the area of composite figures with different shapes?
  2. What is the formula for the area of a parallelogram?
  3. How do congruent shapes affect area calculations?
  4. Can this figure be simplified further for easier calculation?
  5. What are some real-life applications of calculating areas of composite figures?

Tip: When working with composite shapes, break them into simpler geometric shapes to calculate the total area systematically.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Composite Figures
Congruence

Formulas

Area of a square = side^2
Area of a parallelogram = base × height

Theorems

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Suitable Grade Level

Grades 6-8