Find the area of a rhombus whose one side measures 5
cm and one diagonal as 8 cm.
Answers
Answer:
Diagonals bisect each other and they are perpendicular in rhombus
Let half the length of second diagonal be x
As two diagonals and a side form right angled triangle ;
⇒x
2
+4
2
=5
2
⇒x=3
⇒length of 2nd side =2x=6cm
Area of rhombus=
×8×6 =24cm
2
Step-by-step explanation:
Area of Rhombus is 24 cm^2cm
2
Step-by-step explanation:
Properties of Rhombus says-
Diagonals are ⊥ Bisector
Therefore, the diagonal of 8 cm is divided into two segments 4 cm long. Using the Pythagorean Theorem and any of the right triangles to solve for x.
5^2 = 4^2 + x^25
2
=4
2
+x
2
x^2 = 25 - 16x
2
=25−16
x^2 = 9x
2
=9
x = 3
As per the formula for rhombus, Area, A = \frac {1}{2} d_1d_2A=
2
1
d
1
d
2
Where are diagonals
d_1 = 8 cmd
1
=8cm
d_2 = 6 cmd
2
=6cm
A = \frac {1}{2} \times 8 \times 6A=
2
1
×8×6
A = 24\ cm^2A=24 cm
2
