Practice Problems Using Herons Formula :
Here we are going to see some example problems to find the area triangle using herons formula.
If a, b and c are the sides of a triangle, then
the area of a triangle = √s(s − a)(s − b)(s − c) sq.units.
where s = (a + b + c)/2
‘s’ is the semi-perimeter (that is half of the perimeter) of the triangle.
Question 1 :
The perimeter of a triangular plot is 600 m. If the sides are in the ratio 5 : 12 : 13, then find the area of the plot.
Solution :
The sides of triangle be 5x, 12x and 13x.
Perimeter of triangular plot = 600
5x + 12x + 13x = 600
30x = 600
x = 600/30 = 20
5x = 5(20) = 100
12x = 12(20) = 240
13x = 13(20) = 260
s = 600/2 = 300
s - a = 300 - 100 = 200
s - b = 300 - 240 = 60
s - c = 300 - 260 = 40
√s(s − a)(s − b)(s − c) = √300(200)(60)(40)
= √(3 ⋅ 10 ⋅ 10 ⋅ 2 ⋅ 10 ⋅ 10 ⋅ 3 ⋅ 2 ⋅ 10 ⋅ 2 ⋅ 2 ⋅10)
= 12000 m2
Question 2 :
Find the area of an equilateral triangle whose perimeter is 180 cm.
Solution :
Perimeter of equilateral triangle = 180 cm
3a = 180
a = 180/3 = 60 cm
Area of equilateral triangle = (√3/4)a2
= (√3/4)602
= 900√3
= 900(1.732)
= 1558.8 cm2
Question 3 :
An advertisement board is in the form of an isosceles triangle with perimeter 36 m and each of the equal sides are 13 m. Find the cost of painting it at ₹ 17.50 per square metre.
Solution :
Let "x" be the unknown side of the triangle.
Then sides of triangle are x, 13 and 13.
perimeter = 36 m
x + 13 + 13 = 36
x + 26 = 36
x = 36 - 26 = 10 m
a = 10, b = 13 and c = 13
height = √132 - 52
= √(169 - 25)
= √144
height = 12 cm
Area of triangle = (1/2) x base x height
= (1/2) x 10 x 12
= 60 cm2
Cost of of painting it at ₹ 17.50 per square metre
Required cost = 60 (17.50)
= ₹ 1050
After having gone through the stuff given above, we hope that the students would have understood, "Practice Problems Using Herons Formula"
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
Trigonometry 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
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