STD VIII – MENSURATION (Hybrid)

Area of Trapezium and a Polygon

The main components of a triangle’s area are the base and height of the triangle. The base of a triangle can be any side. The height of a triangle is the length of the triangle’s altitude drawn to the chosen base.

The altitude of a triangle is the line a through a vertex which is perpendicular to the opposite side of the triangle.

We can also calculate the area of a triangle without knowing its base and height and given only 3 sides.

Heron, a Greek Engineer and Mathematician in 10 – 70 AD devised a formula to find the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height or half the norm of a cross product of two sides.

In this section we will learn the deduction of areas of the following figures

Area and perimeter of a triangle | Circumference and Area of a Circle

Surface Area, Volume, and Capacity

Volume and Capacity.

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre.

Capacity is the measure of an object’s ability to hold a substance, like a solid, a liquid or a gas. It can be measured in almost every other unit, including liters, gallons, pounds, etc.