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Area of a Triangle


    what you'll learn...

Overview

Area of a Triangle:
12× base ×(height) area of a triangle

type 1

area of a triangle

Consider the triangle given in the figure. The base is 13 cm and height is 8 cm. To find the area of the triangle, compare the triangle with a rectangle of 13 cm by 8 cm.

area of a triangle

The triangle of base 13 cm and height 8 cm is placed over a rectangle of length 13 cm and width 8 cm. It is noted that the triangle splits the rectangle into equal halves. The area of the triangle is half of the area of rectangle OR in other words, 12× base ×(height)

type 2

area of a triangle

Consider the triangle given in the figure. The base is 15 cm and height is 6 cm. To calculate the area, compare the triangle with a rectangle of 15 cm by 6 cm.

area of a triangle

The triangle of base 15 cm and height 6 cm is placed over a rectangle of length 15 cm and width 6 cm.

The rectangle is visualized into two parts ARCP and RBQC

The triangle is visualized into two parts ARC and RBC

It is noted that the area of the triangle ARC is half of the rectangle ARCP and area of the triangle RBC is half of the rectangle RBQC.

The area of the triangle ABC is sum of area of the two triangles ARC and CRB.

= half the area of rectangles ARCP and CRBQ.

=12×AR¯×RC¯+12×RB¯×RC¯

=12×RC¯×(AR¯+RB¯)

=12×RC¯×AB¯)

=12× base × height

The area of the triangle is half of the area of rectangle OR in other words, 12× base ×(height)

type 3

area of a triangle

Consider the triangle given in the figure. The base is 8 cm and height is 6 cm. To calculate the area, compare the triangle with a rectangle covering AQC

area of a triangle

The triangle of base 8 cm and height 6 cm is placed over a rectangle AQCP. The rectangle is visualized to two triangles AQC and APC. The area of triangle AQC is half of the rectangle.

The area of the triangle ABC is

= area of AQC- area of BQC

=12×AQ¯×QC¯- 12×BQ¯×QC¯

=12×QC¯×(AQ¯-BQ¯)

=12×QC¯×AB¯

=12× base × height

The area of the triangle is half of the area of rectangle OR in other words, 12× base ×(height)

common formula

Consider the three types of triangles,
area of a triangle
area of a triangle
area of a triangle

For all the types, the area is derived as

12× base ×(height)

What is the area of the triangle with base 2cm and height 3cm?
The answer is "12×2×3=3cm2"

summary

Area of a Triangle:
12× base ×(height) area of a triangle

Outline

The outline of material to learn "Mensuration basics : Length, Area, & Volume" is as follows.

Note: click here for detailed outline of Mensuration (Basics).

•  Measuring Basics

  →   Introduction to Standards

  →   Measuring Length

  →   Accurate & Approximate Meaures

  →   Measuring Area

  →   Measuring Volume

  →   Conversion between Units of Measure

•  2D shapes

  →   Perimeter of Polygons

  →   Area of Square & rectangle

  →   Area of Triangle

  →   Area of Polygons

  →   Perimeter and area of a Circle

  →   Perimeter & Area of Quadrilaterals

•  3D shapes

  →   Surface Area of Cube, Cuboid, Cylinder

  →   Volume of Cube, Cuboid, Cylinder