Questions and Answers
What is the definition of area in math?
What are the units used to measure the area of a two-dimensional shape?
Why is finding the area of a shape important?
What is an area formula used for?
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What is a square unit?
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What is the shape of the shaded region?
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What is the formula for the area of a circle?
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What is the radius of the circle?
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What is the final step in finding the area of the shaded region?
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What is the formula for finding the area of a rectangle?
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Approximately what is the area of the shaded region?
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What is the process for calculating the area of a two-dimensional geometric figure?
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How can the area of an uncommon shape be found?
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What is the formula for finding the area of a circle with radius r?
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How do you find the area of a shape that is made up of multiple basic shapes?
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Study Notes
What is Area in Math?
- A two-dimensional geometric shape is a flat shape, such as a drawing or a picture.
- The definition of area in math is the space inside of the shape.
- The area of a two-dimensional shape is a measurement of the space inside the shape.
- The area of a two-dimensional shape is measured in square units, or units2.
Square Units
- A square unit is a square with a side length of one unit.
- For example, a square inch is a square that is one inch long on each side.
Formulas for Finding Area
- The formula for finding the area, A, of a square with side length s is: A = s²
- The formula for finding the area of a rectangle with length l and width w is: A = l × w
- The formula for finding the area of a triangle with base b and vertical height h is: A = (b × h) / 2
- The formula for finding the area of a circle with radius r is: A = π × r²
- The formula for finding the area of a parallelogram with base b and vertical height h is: A = b × h
- The formula for finding the area of a trapezoid with bases a and b and vertical height h is: A = ((a + b) × h) / 2
- The formula for finding the area of an ellipse with major axis radius a and minor axis radius b is: A = π × a × b
Finding the Area of Uncommon Shapes
- Not every shape has an area formula.
- The basic area formulas can be used to calculate the area of many uncommon shapes.
- The area of an uncommon shape can be found by dividing the shape into more basic shapes.
How to Calculate Area
- Identify the shape.
- Find the correct area formula.
- Identify the needed measurements.
- Substitute the measurements into the formula.
- Perform the needed calculations.
Area Examples
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Example 1: Find the area of a circle with a radius of 5 inches.
- The area of the circle is approximately 78.5 square inches.
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Example 2: Find the area of a triangle with base 8 cm and height 3 cm.
- The area of the triangle is 12 square centimeters.
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Example 3: Find the area of a shape made up of a rectangle and a triangle.
- The area of the shape is 55 square inches.
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Example 4: Find the area of the shaded region of a shape.
- The area of the shaded region is approximately 72 square centimeters.
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Description
Learn about the definition and measurement of area in two-dimensional shapes, including the importance of squared units.