Applications : Area of a triangle and parallelogram

Applications: Area of Triangle and Parallelogram

Understanding the Basics

Triangles and parallelograms are types of polygons used across various areas of mathematics.
The area of a shape is the amount of space it occupies.
By understanding the formulas to calculate the area of these shapes, we can solve real-life and mathematical problems.

Area of a Triangle

The area of a triangle can be found using the formula 1/2 base * height.
It refers to the number of square units that can fit within the triangle.
The base of the triangle can be any of its sides, and the height must be measured perpendicular to the base.

Derivation of the Triangle Area Formula

For a triangle with base b and height h, imagine two identical triangles placed side by side to form a rectangle.
The rectangle’s area is base * height (b * h). Since the triangle is half this rectangle, the area becomes 1/2b * h.

Area of a Parallelogram

The area of a parallelogram can be determined with the formula base * height.
Unlike triangles, the base and height in parallelograms should be perpendicular to each other.

Derivation of the Parallelogram Area Formula

For a parallelogram with a base of b and a height of h, cut off the triangle at one end and attach it to the other end, forming a rectangle.
The rectangle’s area is b * h, which is also the area of the original parallelogram.

Uses of the Formulas

The formulas for the area of triangles and parallelograms have broad applications in geometry, engineering, architecture, and computing.
In geometry, they are essential for calculations related to the space within or shared by multiple shapes.

Remember that understanding and correctly applying these formulas is key to solving area problems in Further Maths. Always ensure that you’re using the correct base and height for your calculations.