Math Problem Statement

Find the area of each object: a. A square with side 4 cm. b. A triangle with a base and height of 4 cm. c. A circle with radius 4 cm. Use 3.14 for π.

Solution

Let's solve each part:

  1. Square with side 4 cm: Area=side2=4×4=16cm2\text{Area} = \text{side}^2 = 4 \times 4 = 16 \, \text{cm}^2

  2. Triangle with base and height of 4 cm: Area=12×base×height=12×4×4=8cm2\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 4 = 8 \, \text{cm}^2

  3. Circle with radius 4 cm (using π=3.14\pi = 3.14): Area=π×radius2=3.14×42=3.14×16=50.24cm2\text{Area} = \pi \times \text{radius}^2 = 3.14 \times 4^2 = 3.14 \times 16 = 50.24 \, \text{cm}^2

The answers are:

  • a. 16 cm²
  • b. 8 cm²
  • c. 50.24 cm²

Would you like more details on any of these solutions?

Here are some related questions to expand understanding:

  1. How would the area change if the side of the square was doubled?
  2. What is the formula for the area of a triangle when only the lengths of the sides are known?
  3. How does the value of π\pi impact the area of a circle calculation?
  4. How can you find the area of a triangle if only one angle is given along with two sides?
  5. What are some real-world applications of calculating areas of these shapes?

Tip: When calculating areas, always remember to square the relevant measurements and check units.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation

Formulas

Area of a square = side^2
Area of a triangle = 1/2 * base * height
Area of a circle = π * radius^2

Theorems

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Suitable Grade Level

Grades 5-7