Area of Rhombus
Here we will learn how to find the area of rhombus.
ABCD is a rhombus whose base AB = b, DB ⊥ AC DB = d_{1} AC = d_{2} and the altitude from C on AB is CE, i.e., h.
Area of rhombus ABCD = 2 Area of ∆ ABC = 2 × 1/2 AB × CD sq units. = 2 × 1/2 b × h sq. units = base x height sq. units
Also, area of rhombus = 4 × area of ∆ AOB = 4 × 1/2 × AO × OB sq. units = 4 × 1/2 × 1/2 d_{2} × 1/2 d_{1} sq. units = 4 × 1/8 d_{1} × d_{2} square units = 1/2 × d_{1} × d_{2}; where d_{1} and d_{2} are diagonals. Therefore, area of rhombus = 1/2 (product of diagonals) square units
• Perimeter of rhombus = 4 × side
Workedout examples on area of rhombus:
1. Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.
Solution:
ABCD is a rhombus in which AB = BC = CD = DA = 17 cm AC = 16 cm
Therefore, AO = 8 cm In ∆ AOD, AD^{2} = AO^{2} + OD^{2} ⇒ 17^{2} = 8^{2} + OD^{2} ⇒ 289 = 64 + OD^{2} ⇒ 225 = OD^{2} ⇒ OD = 15 Therefore, BD = 2 OD = 2 × 15 = 30 cm Now, area of rhombus
= 1/2 × d_{1} × d_{2} = 1/2 × 16 × 30 = 240 cm^{2}
2. Find the altitude of the rhombus whose area is 315 cm^{2} and its perimeter is 180 cm.
Solution: Since, the perimeter of rhombus = 180 cm Therefore, side of rhombus = P/4 = 180/4 = 45 cm Now, area of rhombus = b × h ⇒ 315 = 45 × h ⇒ h = 315/45 ⇒ h =7 cm Therefore, altitude of the rhombus is 7 cm.
3. The floor of building consists of 2000 tiles which are rhombus shaped and each of its diagonals are 40 cm and 25 cm in length. Find the total cost of polishing the floor, if the cost per m^{2} is $5.
Solution:
In each rhombus, the tile length of the diagonals = 40 cm and 25 cm Therefore, area of each tile = 1/2 × 40 × 25 = 500 cm^{2} Therefore, area of 2000 tiles = 2000 × 500 cm^{2} = 1000000 cm^{2} = 1000000/10000 cm^{2} = 100 m^{2} For 1 m^{2} cost of polishing = $5 = $5 × 100 = $500.
The formula of perimeter and area of rhombus are explained above with the detailed stepbystep explanation using various examples.
● Mensuration Area and Perimeter Perimeter and Area of Rectangle Perimeter and Area of Square Area of the Path Area and Perimeter of the Triangle Area and Perimeter of the Parallelogram Area and Perimeter of Rhombus Area of Trapezium Circumference and Area of Circle Units of Area Conversion Practice Test on Area and Perimeter of Rectangle Practice Test on Area and Perimeter of Square
● Mensuration  WorksheetsWorksheet on Area and Perimeter of Rectangles Worksheet on Area and Perimeter of Squares Worksheet on Area of the Path Worksheet on Circumference and Area of Circle Worksheet on Area and Perimeter of Triangle
7th Grade Math Problems
8th Grade Math Practice
From Area of Rhombus to HOME PAGE
