The area of the rhombus ABCD is 24.7 cm².
The length of diagonal BD is 6.5 cm.
What is the area of a rhombus?
A rhombus have equal four sides and the diagonals of the rhombus divides it into four equal right triangles. The area of the rhombus is the sum of individual areas of the four right triangles.
The hypotenuse side of the right triangle = side of the rhombus = BC = 5 cm
- One of the legs of the right triangle = AO = OC = 3.8 cm
- Let the second leg of the right triangle = OB = OD = x
The second leg of the right triangle is calculated as follows;
[tex]x^2 + 3.8^2 = 5^2\\\\
x^2 = 5^2 - 3.8^2 \\\\
x^2 = 10.56\\\\
x = \sqrt{10.56} \\\\
x = 3.25 \ cm[/tex]
The area of one right triangle of the rhombus is calculated as follows;
[tex]A = \frac{1}{2} (3.8)(3.25)[/tex]
The area of the rhombus ABCD is calculated as follows;
[tex]A = 4 \times \frac{1}{2} (3.8)(3.25)\\\\
A = 24.7 \ cm^2[/tex]
The length of diagonal BD is calculated as follows;
[tex]BD = OB \ + \ OD\\\\
BD = x \ + \ x\\\\
BD = 3.25 \ cm \ + \ 3.25 \ cm\\\\
BD = 6.5 \ cm[/tex]
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