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A = angle A a = side a B = angle B b = side b C = angle C c = side c A = B = C = 60° a = b = c K = area P = perimeter s = semiperimeter h = altitude *Length units are for your reference only since the value of the resulting lengths will always be the same no matter what the units are. Calculator UseAn equilateral triangle is a special case of a triangle where all 3 sides have equal length and all 3 angles are equal to 60 degrees. The altitude shown h is hb or, the altitude of b. For equilateral triangles h = ha = hb = hc. If you have any 1 known you can find the other 4 unknowns. So if you know the length of a side = a, or the perimeter = P, or the semiperimeter = s, or the area = K, or the altitude = h, you can calculate the other values. Below are the 5 different choices of calculations you can make with this equilateral triangle calculator. Let us know if you have any other suggestions! Formulas and Calculations for a equilateral triangle:
1. Given the side find the perimeter, semiperimeter, area and altitude
2. Given the perimeter find the side, semiperimeter, area and altitude
3. Given the semiperimeter find the side, perimeter, area and altitude
4. Given the area find the side, perimeter, semiperimeter and altitude
5. Given the altitude find the side, perimeter, semiperimeter and area
For more information on triangles see: Weisstein, Eric W. "Equilateral Triangle." From MathWorld--A Wolfram Web Resource. Equilateral Triangle. Weisstein, Eric W. "Altitude." From MathWorld--A Wolfram Web Resource. Altitude.
We will discuss here how to find the perimeter of a triangle. We know perimeter of a triangle is the total length (distance) of the boundary of a triangle. Perimeter of a triangle is the sum of lengths of its three sides. For example, perimeter of the ∆PQR = PQ + QR + RP ● The perimeter of a triangle ABC = AB + BC + CA = 2 cm + 4 cm + 3 cm, (add the length of each side of the triangle). = 9 cm Perimeter of the triangle = Sum of the sides.
● A triangle has 3 sides The perimeter of the triangle XYZ = 3 cm + 5 cm + 4 cm = 12 cm The perimeter of the triangle = Sum of the lengths of three sides. Let us consider some of the examples on perimeter of a triangle: 1. Find the perimeter of a triangle having sides 3 cm, 8 cm and 6 cm. Solution: Perimeter of a triangle = Sum of all the three sides = AB + BC + AC = 3 cm + 8 cm + 6 cm = 17 cm 2. Find the perimeter of the triangle PQR whose sides are 4 cm, 6 cm and 8 cm. Solution: In the figure PQ = 4 cm, PR = 6 cm and QR = 8 cm The perimeter of the rectangle PQR = 4 cm + 6 cm + 8 cm = 18 cm 3. Find the perimeter of an equilateral triangle whose one side is 5 cm. Solution: A triangle in which all the sides are equal is called an equilateral triangle. Perimeter of the equilateral triangle = 3 × side = 3 × 5 cm = 15 cm Thus, perimeter = 15 cm. 4. Find the perimeter of a triangle whose length of three sides are 8 cm, 11 cm, 13 cm. Solution: To find the perimeter of the triangle, we add all the sides together. Perimeter of a triangle = Sum of all the three sides = 8 cm + 11 cm + 13 cm = 32 cm 5. Find the perimeter of a triangle whose sides are 5 cm, 2 cm and 3 cm. Solution: Perimeter of the triangle is the sum of the lengths of its sides. Perimeter = 5 cm + 2 cm + 3 cm Thus, perimeter = 10 cm. 6. Find the perimeter of each triangle. Solution: (i) Perimeter of ∆XYZ = 5.5 cm + 6 cm + 6 cm = 17.5 cm (ii) Perimeter of ∆ABC = 8 cm + 6 cm + 6 cm = 20 cm (iii) Perimeter of ∆PQR = 4 cm + 3 cm + 5 cm = 12 cm 7. Find the perimeter of the given shapes. Solution: (i) Perimeter = PQ + QR + RS + ST + TU + UV + VP = 2.5 cm + 3 cm + 2 cm + 3 cm + 2.5 cm + 4 cm + 4 cm = 21 cm (ii) Perimeter = PQ + QR + RS + SP = 4 cm + 4 cm + 4 cm + 4 cm = 16 cm (iii) Perimeter = PQ + QR + RS + ST + TP = 7 cm + 6 cm + 4 cm + 3 cm + 5 cm = 25 cm Word Problems on Perimeter of a Triangle: 1. Two sides of a triangle are 3 cm and 4 cm. Find the third side of the triangle if its perimeter is 11 cm. Solution: First side of the triangle = 3 cm Second side of the triangle = 4 cm Perimeter of the triangle = Sum of the lengths of sides i.e. sum of the lengths of the sides = 11 cm 3 cm + 4 cm + length of the third side = 11 cm 7 cm + length of the third side = 11 cm But we know that 7 cm + 4 cm = 11 cm (Note: 11 – 7 = 4) Therefore, length of the third side = 4 cm Questions and Answers on Perimeter of a Triangle: 1. A triangle has a perimeter of 50 cm. If its two sides are of lengths 15 cm and 19 cm, what is the length of the third side? Answer: 16 cm
● Related Concepts ● Units for Measuring Length ● Measuring Instruments ● To Measure the Length of a Line-segment ● Perimeter of a Figure ● Perimeter of a Triangle ● Perimeter of a Rectangle ● Perimeter of a Square ● Unit of Mass or Weight ● Examples on Unit of Mass or Weight ● Units for The Measurement of Capacity ● Examples on Measurement of Capacity ● Measurement of Time ● Read a Watch or a Clock ● Antemeridian (a.m.) or Postmeridian (p.m.) ● What Time it is? ● Time in Hours and Minutes ● 24 Hour Clock ● Units of Time ● Examples Units of Time ● Time Duration ● Calendar ● Reading and Interpreting a Calendar ● Calendar Guides us to Know 4th Grade Math Activities From Perimeter of a Triangle to HOME PAGE
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