Areas of Parallelograms and Triangles • Topic 1 of 3

Meaning of Area

What is the Meaning of Area?

In simple English, area is the measure of the total flat surface enclosed inside a closed two-dimensional shape. Think of it as the amount of paint needed to color a drawing completely, or the number of identical floor tiles required to completely cover a room's floor without any overlaps or gaps.

While perimeter measures the length of the outer boundary line (like a fence around a park), area measures the space trapped inside that boundary line.

To build a solid foundation, let us look at the fundamental rules governing area:

  • The Planar Region: A simple closed curve splits a plane into an inner region and an outer region. The flat surface together with its boundary is called a planar region, and its measurement magnitude is its area.
  • Unit of Measurement: Area is always measured in square units, such as square centimeters (sq cm) or square meters (sq m).
  • Congruence Area Property: If two geometric figures are perfectly identical, they are congruent. If figure A is congruent to figure B, then the area of figure A must be exactly equal to the area of figure B.
  • Area Addition Property: If a large planar region is broken down into smaller, non-overlapping parts, the total area of the large figure is exactly equal to the sum of the individual areas of all its smaller pieces.

Let us compare the core structural differences between perimeter and area:

FeaturePerimeterArea
**Real-life example**Fencing wire around a garden patchGrass carpet covering the ground
**Dimension**One-dimensional (1D)Two-dimensional (2D)
**Standard units**cm, m, kmsq cm, sq m, sq km
Area of Parallelogram = Base × Heighthb (base)→ Shear to= b × hArea of Parallelogram = Base × HeightA = b × h (where h is perpendicular height, NOT the slant side)Triangle with same base and height: Area = ½ × b × hA parallelogram diagonal divides it into 2 equal area triangles
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Worked Example

Solve a standard problem on Meaning of Area.

Solution

Apply the formula/method shown in the concept section above.

Key Points

  • Understand the definition and properties of Meaning of Area.
  • Study the worked examples and practice similar problems.
  • Always verify your answer using the original conditions.
Tap an option to check your answer0 / 4
Q1.Area is measured in:
Explanation: Square units.
Q2.Congruent figures have:
Explanation: Equal areas.
Q3.Two figures with equal area are:
Explanation: Equal area does not imply congruence.
Q4.The area of a region cannot be:
Explanation: Area is non-negative.