Question

a rhombus has a perimeter of 100 M and a diagonal 30 M long find the area of the Rhombus

Answer 1

Area of the Rhombus is 600 cm².

• Perimeter of the Rhombus is given as 100M.
• Rhombus has all sides equal.
• Therefore, 4(side) = 100

side = 25cm

• Each side of the rhombus is 25 cm.

• We have to find the area of the Rhombus. To find the area of the Rhombus we need to find the diagonals of the Rhombus.

• One diagonal is given as 30 cm.

• We have to find the length of other diagonal.

• The diagonals of a Rhombus are perpendicular bisectors of each other. Therefore sum of square of half the length of one diagonal and square of length of half of other diagonal is equal to square of the side.(Using Pythagoras Theorem)

(d/2)²+15² = 25²

(d/2)² = 625-225 =400

d/2 = 20

d = 40

• Length of other diagonal is 40 cm.
• Now area of rhombus is equal to product of both the diagonals divided by 2.

Area of rhombus = 30×40÷2 = 600 cm².

• Area of the rhombus is 600 cm².

Answer 2

Answer:

Perimeter of rhombus=100m

□D1=30m

To find:

○Area of rhombus=?

perimterofrhombus=100m

=)4×a=100

=)a= 100/4

=)a=25m

inaright△ofrhombus

h 2 =p2 +b2

=)25^2 =15^2

+b^2

=)625−225=b2

=)b= √400

=)b=20m

d2=2×b=2×20=40m

areaofrhombus= 1/2×d1×d2

=) 1/2 ×30×40

=)15×40

=)600m2

Hope this is helpful for you