Fix the mistake: Plane Figures (Area and Angles)

Plane Figures ① Basic Area Formulas

In this lesson, we will organize the area formulas for triangles, quadrilaterals, circles, and other shapes, and learn how to apply them to problems.

Basic Area Formulas

  • Rectangle: length × width
  • Square: side × side
  • Parallelogram: base × height
  • Triangle: base × height ÷ 2
  • Trapezoid: (upper base ＋ lower base) × height ÷ 2
  • Rhombus: diagonal × diagonal ÷ 2
  • Circle: radius × radius × π（≒3.14）
Example 1
Find the area of a triangle with a base of 8cm and a height of 5cm.

Answer:
8×5÷2＝20cm²
Example 2 (Application)
A triangle with a base of 8cm and a height of 6cm is inside a rectangle measuring 10cm vertically and 8cm horizontally. Find the area outside the triangle (the remaining part of the rectangle).

Answer:
Area of the rectangle: 10×8＝80cm²
Area of the triangle: 8×6÷2＝24cm²
Remaining area: 80－24＝56cm²
Key Points
  • The basic formula is “base × height.” ÷2 is used only for triangles and trapezoids.
  • Solve composite figures by using “larger shape － smaller shape” or by “dividing the figure into parts.”
  • Use 3.14 for pi unless the problem specifies otherwise.

Practice Problems

  1. Find the area of a trapezoid with an upper base of 4cm, a lower base of 10cm, and a height of 6cm.
  2. Find the area of a circle with a radius of 5cm. (π＝3.14)

Answers and Explanations

  1. Answer:42cm²
    Explanation: Area of a trapezoid＝(upper base ＋ lower base) × height ÷ 2＝(4＋10)×6÷2＝14×6÷2＝42cm².
  2. Answer:78.5cm²
    Explanation: Area of a circle＝radius × radius × π＝5×5×3.14＝78.5cm².

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