Area, Surface Area, and Volume of Geometric Shapes

Study Notes

Area, Surface Area, and Volume of Geometric Shapes

This article aims to provide a comprehensive understanding of the area, surface area, and volume calculations for various geometric shapes, including triangles, circles, rectangles, and squares. Additionally, we will explore the concept of volume in a cylindrical shape.

Area of Triangle

In a triangle, the area is calculated based on the length of the base and the height. For an equilateral triangle, the formula is Area = (sqrt(3)/4) * side^2.

Volume of Triangle (as a prism)

To find the volume of a triangular prism, we can apply the formula Volume = (1/2) * base length * height * length. This formula considers the area of one of the triangle bases, multiplied by the height of the prism and the length between the two triangular bases.

Surface Area of Circle

For a circle, the surface area can be determined as 2πr², where 'r' represents the radius of the circle.

Surface Area of Rectangle

The surface area of a rectangle is calculated by multiplying the length of the rectangle (width) by the width of the rectangle itself.

Area of Square

Since a square is simply a regular quadrilateral with four congruent sides and four right angles, its area is simply the square of the length of one side. Thus, Area = side^2.

Volume of Rectangle

The volume of a rectangular prism is calculated using the formula Volume = length × width × height.

Volume of Cylinder

The volume of a cylinder can be computed using the formula V = π r² h, where 'r' represents the radius of the base circle and 'h' stands for the height of the cylinder.

Description

Explore the calculations for area, surface area, and volume of geometric shapes such as triangles, circles, rectangles, squares, triangular prisms, rectangular prisms, and cylinders. Learn the formulas and concepts related to determining measurements for each shape.