9th Class Mathematics Areas of Parallelograms and Triangles Area of Parallelogram & Triangle

AREA OF PARALLELOGRAM AND TRIANGLE

FUNDAMENTALS

• The area of a parallelogram is the product of its base and the corresponding altitude.

Area of parallelogram \[=\frac{1}{2}\times CD\times AE\]

• Parallelogram on the same base and between the same parallels are equal in areas.

i.e., Area of parallelogram PQRS = Area of Parallelogram SRTU.

• A diagonal of a parallelogram divides it into two triangles of equal areas.

Area of \[\Delta ABD\] = Area of \[\Delta BCD\]

• The area of a triangle is half the product of any of its side and the corresponding altitude.

Area of \[\Delta ABC=\frac{1}{2}(BC\times AD)\]

• Triangles on the same base and between the same parallel lines are equal in area.

i.e., Area of \[\Delta PQR\] = Area of \[\Delta QRS\]

• The area of trapezium is half the product of its altitude and sum of parallel lines.

Area of trapezium \[ABCD=\frac{1}{2}(AB+CD)\times AE\]

• The area of a rhombus is half the product of the lengths of its diagonals.

Area of Rhombus \[=\frac{1}{2}AC\times BD\]

• A median of a triangle divides it into two triangles of equal area.

Area of \[\Delta PQS=\Delta PRS\].

• Area of equilateral triangle is equal to\[\frac{\sqrt{3}}{4}{{a}^{2}}\], where a is the side of the triangle.
• If the medians of \[\Delta ABC\] intersect at G, Then

Area of \[\Delta AGB\]= Area of \[\Delta BGC\]

= Area of\[\Delta AGC\].

• The formula given, by heron about the area of triangle is known as heron’s formula. It is stated as Area of triangle= \[\sqrt{s(s~-a)(s-b)(s~-c)}\]

Where a, b, c are the sides of the triangle and s is semiperimetre. i.e., half of the perimeter of the triangle= \[\frac{a+b+c}{2}\]