Area and Perimeter of Triangle
Perimeter of a Triangle
We can find the length of the fencing required for a triangular park by finding the perimeter of the triangle.
A serving tray as shown forms an equilateral triangle – that is, a triangle with three equal sides. Let each side be 20 cm long.
To find the total length of a decorative lace to be pasted on outside borders, one needs to find the perimeter of the triangle. Since all the three sides of the triangle are of equal length, we can find the perimeter by multiplying the length of each side by 3.
20 + 20 + 20 = 3 × 20 = 60 cm.
Thus, the perimeter of an equilateral triangle is 3 times the length of each side.
Area of a triangle
Area of a two-dimensional shape is the space occupied by the shape. This area can be found by dividing the shape into unit squares and determining the number of unit squares in the shape as each unit square occupies one square unit space.
Consider a rectangle of length 4 cm and width 3 cm. It can be filled with 3 rows and 4 columns of unit squares and therefore the area is 3 times 4 or 12 square centimeter. That is, the area of a rectangle is the product of its length and width.
A rectangle can be divided into two congruent triangles.
So, the area of each triangle is half the area of the rectangle. That is 1⁄2 x l x w.
Consider a scalene triangle △ABC. Note that, to write the area of a triangle as half the area of a rectangle, we need to have the height perpendicular to the base. So, draw a perpendicular from a vertex to the opposite side.
Here, BD is the perpendicular drawn from the vertex B to the opposite side AC.
Thus, the area of a triangle is half the product of its base and height.