Question: Find the height of a rhombus, whose perimeter is 22cm and whose area is 16.5cm^2.?
rhombus Definition:
A rhombus is a four-sided polygon in which every side has the same length. It is an equilateral quadrilateral.
Rhombus Formula :
Base Times height Method : area of Rhombus = b * h
Diagonal Method : Area of Rhombus = ½ * d1 * d2
Trigonometry Method : Area of Rhombus = a² * SinA
perimeter of Rhombus = 4(a)
where
a = side, b = breadth, h = height, d1, d2 are diagonals
Rhombus Image/Diagram
Rhombus Example :
Case 1: Find the area of a rhombus with the given base 3 and height 4 using Base Times Height Method.
Step 1: Find the area.
Area = b * h = 3 * 4 = 12.
Case 2: Find the area of a rhombus with the given diagonals 2, 4 using Diagonal Method.
Step 1: Find the area.
Area = ½ * d1 * d2 = 0.5 * 2 * 4 = 4.
Case 3: Find the area of a rhombus with the given side 2 using Trigonometry Method.
Step 1: Find the area.
Area = a² * SinA = 2² * Sin(33) = 4 * 1 = 4.
Case 4: Find the perimeter of a rhombus with the given side 2.
Step 1: Find the perimeter.
Perimeter = 4(a) = 4 * 2 = 8.
The above example will clearly illustrates how to calculate the Area, Perimeter of a Rhombus manually.
Relation Questions:
Answer:
A rhombus has four equal sides. therefore, the base is 22/4 or 5.5cm. The area can be found by taking the area of the side times the height. Therefore if you have the area and divide it by the side length, you will get the height. 16.5 / 5.5 = 3 The height is 3cm.