AREA OF TRIANGLES AND QUADRILATERALS
About "Area of Triangles and Quadrilaterals"
Area of Triangles and Quadrilaterals :
In this section, we are going to learn, how to find area of a triangle and a quadrilateral.
The following postulates can be used to prove several area theorems.
Area Postulates
Area of a Square Postulate :
The area of a square is the square of the length of its side, or A = s2.
Area Congruence Postulate :
If two polygons are congruent, then they have the same area.
Area Addition Postulate :
The area of a region is the sum of the areas of its non overlapping parts.
Area Theorems
Theorem 1 (Area of a Rectangle) :
The area of a rectangle is the product of its base and height.
That is,
Area = b ⋅ h
Theorem 2 (Area of a Parallelogram) :
The area of a parallelogram is the product of a base and its corresponding height.
That is,
Area = b ⋅ h
Theorem 3 (Area of a Triangle) :
The area of a triangle is one half the product of a base and its corresponding height.
That is,
Area = 1/2 ⋅ b ⋅ h
Theorem 4 (Area of a Trapezoid) :
The area of a trapezoid is one half the product of the height and sum of the bases.
That is,
Area = 1/2 ⋅ h ⋅ (b1 + b2)
Theorem 5 (Area of a Kite) :
The area of a kite is one half the product of the lengths of its diagonals.
That is,
Area = 1/2 ⋅ d1 ⋅ d2
Theorem 6 (Area of a Rhombus) :
The area of a rhombus is one half the product of the lengths of its diagonals.
That is,
Area = 1/2 ⋅ d1 ⋅ d2
Proof of the Area a Parallelogram
The area of a parallelogram is the area of a rectangle with the same base and height.
It has been illustrated in the diagram given below.
Proof of the Area a Triangle
The area of a triangle is half the area of a parallelogram with the same base and height.
It has been illustrated in the diagram given below.
Proof of the Area a Trapezoid
The area of a trapezoid is half the area of the parallelogram with the same height and a base length is equal to sum of the base lengths of the trapezoid.
It has been illustrated in the diagram given below.
Proof of the Area a Kite
The area of a kite is half the area of the rectangle whose length and width are the lengths of the diagonals of the kite.
It has been illustrated in the diagram given below.
Proof of the Area a Rhombus
The area of a rhombus is half the area of the rectangle whose length and width are the lengths of the diagonals of the rhombus.
It has been illustrated in the diagram given below.
Apart from the stuff given above, if you need practice problems on area of triangles and quadrilaterals,
After having gone through the stuff given above, we hope that the students would have understood, "Area of Triangles and Quadrilaterals".
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Time and work word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Recent Articles
-
Formula for a Squared minus b Square
Aug 17, 19 07:24 AM
Formula for a Squared minus b Square - Example Problems and Step by Step Solutions
-
Formula for a plus b Whole Square
Aug 17, 19 06:39 AM
Formula for a plus b Whole Square - Example Problems and Step by Step Solutions
-
Formula for a minus b Whole Square
Aug 17, 19 06:35 AM
Formula for a minus b Whole Square - Example Problems and Step by Step Solutions
