Secondary School Maths - Volumes, Areas and Perimeters of Figures

May 26, 2017 FLAI40 Leave a comment

This posting is for those children still studying in secondary schools. Help them to improve their skills in Mathematics by letting them read this posting.

The volume of a solid figure is the amount of space displaced by this figure. Volume is measured in cubic units.

A cube, for instance, with sides of 5 centimeters (5 cm), has a volume of (Side) cubed or 5 cm

5 cm x 5 cm x 5 cm = 125 cubic cm. (125 cm3). S cubed.

The volume of a cuboid with measurements of length ( L ), breadth ( B ) and height ( H ) is:

(L x B x H).

For instance, a cuboid of 7 cm (Length), 5 cm (Breadth) and 2 cm (Height), has a volume of 70 cm2 as follows: Volume = 7 cm x 5 cm x 2 cm = 70 cubic cm.

The area of a simple closed figure like a triangle, a square or a rectangle is the amount of space inside the closed lines. Areas are measured in square units.

A rectangle, for instance, with 7 centimeters length (L = 7 cm), and 5 centimeters breadth (B = 5 cm) has an area of (L x B) or 7 cm x 5 cm = 35 square cm. (35 cm2).

A square, for instance, with sides of 7 centimeters, has an area of 7 cm x 7 cm = 49 cm2.

How about the area of a triangle? The formula for the area of a triangle is half the base of the triangle multiplied by the height of the triangle.

Let us say that a triangle has sides measuring 15 centimeters, 14 centimeters, and 11 centimeters, and the height with the base of 11 centimeters being 13.36 centimeters, what is the area of this triangle?

1/2 (half) x base (11 cm) x height (13.36 cm).

= 73.48 sq. cm. (73.48 cm2).

http://www.mathwarehouse.com/geometry/triangles/area/index.php

Perimeter Formulae
Shape	Formula	Variables
Square	$P = 4 s$	$s$ is the length of the side of the square.
Rectangle	$P = 2 L + 2 W$	$L$ and $W$ are the lengths of the rectangle’s sides (length and width).
Triangle	$a + b + c$	$a, b$ and $c$ are the side lengths.
Right Triangle, with legs $a$ and $b$	$P = a + b + \sqrt{a^{2} + b^{2}}$	$a$ and $b$ are the lengths of the two legs of the triangle
Circle	$P = C = 2 π r = π d$	$r$ is the radius and $d$ is the diameter.

Area Formulae

Square

$A = s^{2}$

Rectangle

A = L x W - L and W are the lengths of the rectangle’s sides.

Triangle

A = half base (B) x height (h)

or, if the three sides are known, first find out the value of s.

s = half of the total of the three sides.

Then the area is the square root of s x (s-a) x (s-b) x (s-c) the a, b, c being the three sides of the triangle.

For example, if the sides of the triangle is 11 cm, 14 cm and 15 cm,

s = half of (11 + 14 + 15) = 20

s - a = 20 - 11 = 9

s - b = 20 - 14 = 6

s - c = 20 - 15 = 5

s x (s-a) x (s-b) x (s-c) = 20 x 9 x 6 x 5 = 5,400

square root of 5,400 = 73.48 square cm

Parallelogram

Area = length of base (b) x height (h)

Trapezoid

Area = half of (b1 + b2) x height (h),

b1 and b2 been the lengths of the two parallel sides.

Circle

Area = Pi x radius (r) squared

= 3.142 x r2

Volume Formulas


Shape	Formula	Variables
Cube	$V = s^{3}$	$s$ is the length of the side.
Right Rectangular Prism	$V = L W H$	$L$ is the length, $W$ is the width and $H$ is the height.
Prism or Cylinder	$V = A h$	$A$ is the area of the base, $h$ is the height.
Pyramid or Cone	$V = \frac{1}{3} A h$	$A$ is the area of the base, $h$ is the height.
Sphere	$V = \frac{4}{3} π r^{3}$	$r$ is the radius.

tagged with area, Maths, perimeter, secondary school maths, solids, volume

Secondary School Maths - Volumes, Areas and Perimeters of Figures

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