Area of triangle

Area of triangle

Area of triangle

Total surface covered by a triangle is called the area of triangle. To find the area of a triangle we can do the following activities:
Activities to find the formula for area of triangle
i.              Take a paper in triangle shape of base (b) and height (h) as shown in the figure.
ii.            Cut horizontally through middle of the perpendicular as shown in figure.
iii.           Cut upper part into two small triangles through perpendicular as shown in the figure.
iv.           Arrange  the small triangles in one place to form a rectangle ABCD as shown in the figure.
v.             The rectangle ABCD so formed will have the length equal to b and breadth equal to h/2 as shown in the figure.
          Area of Δ = Area of rectangle ABCD
                                           = BC × CD
                                           = b × h/2
                                           = ½ × b × h
          Area of Δ = ½ × b × h

Area of right angled ΔABC = ½ × b × pArea of a right angled triangle

When the triangle is a right angled triangle then height (h) = perpendicular (p), therefore the area of triangle = ½ × base × perpendicular
i.e           area of Δ = ½ × b × p

equilateral triangle ABCArea of an equilateral triangle

In the given figure, ΔABC is an equilateral triangle and AMBC.
If AB = BC = AC = a then BM = CM = a/2

Isosceles triangle ABCArea of an isosceles triangle

In isosceles ΔABC, AB = AC = a and base BC = b
Then AMBC is drawn. Thus BM = CM = b/2Area of an isosceles triangle

Area of scalene triangle

If a, b and c are three sides of a scalene triangle then

Area of scalene triangle




Workout Examples

Example 1: Find area of the triangle given below:
triangle ABC of base 12 cm and height 6 cm

Solution:
                From the figure,
                Base (b) = 12 cm
                Height(h) = 6 cm
                we know,
                                Area of triangle = ½ × b × h
                                                    = ½ × 12cm × 6 cm
                                                    = 36 cm2

Example 2: Find area of the triangle given below:
equilateral triangle of length 6 cm

Solution:
                Given figure is an equilateral triangle where
                a = 6 cm
                we know,
area of equilateral triangle

                                

Example 3: Find the area of the triangle given below:
Triangle ABC

Solution:
                Given figure is an isosceles triangle where
                Base(b) = 8 cm
                Two equal sides (a) = 5 cm
                we know,
                                
area of isosceles triangle





Example 4: Find the area of the triangle ABC given below.
scalene triangle ABC of lengths 6 cm, 10 cm and 8 cm

Solution:
                In triangle ABC,
                                a=10cm, b=8cm and c=6cm
area of scalene triangle

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