Volume of a Cube using formula

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and of trigonal trapezohedron. The cube is dual to the octahedron. It has cubical symmetry (also called octahedral symmetry). A cube is the three-dimensional case of the more general concept of a hypercube.The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically. One-dimensional figures (such as lines) and two-dimensional shapes such as square (geometry help) squares are assigned zero volume in the three-dimensional space. Volume is commonly presented in units such as cubic meters, cubic centimeters, litres, or millilitres.Let's see how to find the volume of a cube by using formula for volume
Question:-

If the edge of the cube is 10 m ,then what is the volume of the cube?

Answer:-

Given the edge as 10m

in a cube all the edges are same

so the length of the cube=10m

Width of the cube= 10m

height of the cube = 10m

Volume formula is

length x width x height

so the volume of the given cube is

10 x 10 x 10 = 30 m³

How to find the area of a quadrilateral

a quadrilateral is a polygon with four 'sides' or edges and four vertices or corners. Sometimes, the term quadrangle is used, for analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on. The word quadrilateral is made of the words quad and lateral. Quad means four and lateral means sides. The interior angles of a quadrilateral add up to 360 degrees of arc.Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting). Simple quadrilaterals are either convex or concave.

Two identical isosceles triangles with side length 5 cm are joined at their bases with length 8 cm .What is the area of the quadrilateral.


a²+b²=c²

4²+b²=5²

16+b²=25

b²=25-16

b²=9

b=√9=3

Now by using area of triangle formula let's find the area of ABC ,which is
a part of the quadrilateral
Area of Δ ABC=1/2 (8)(3)

= 4*3=12 square units

Area of quadrilateral ABCD=12+12 =24 square units

problem on rotation of a triangle about 90 degrees

Topic:-Rotation of a triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three side s or edges which are line segments. A triangle with vertices A, B, and C is denoted ABC.

We can rotate this triangle ,when we have the vertices of triangle ,based on the origin of triangle.

This geometry help will give a example problem.

Question:-

Rotate a triangle A with vertices (1,0),(2,1),(3,-2)by 90 degrees about the origin

Answer:-

Rotation by 90° about the origin : R(origin,90°)


A rotation by 90° about the origin can be seen in the picture below in which A is rotated to it's image A^| .The general rule for rotation by 90° about the origin is (A,B)-->(-B,A)

















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