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Question
If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm2.
Options
True
False
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Solution
This statement is True.
Explanation:
To find the area of rhombus, we divide it into two triangles.
As all the sides of a rhombus are equal, we have for a triangle
a = 10, b = 10, c = 16
`s = (a + b + c)/2`
⇒ `s = (10 + 10 + 16)/2 = 36/2 = 18`.
Area (Δ) = `sqrt(s(s - a)(s - b)(s - c))`
⇒ Area (Δ) = `sqrt(18(18 - 10)(18 - 10)(18 - 16))`
⇒ Area (Δ) = `sqrt(18 xx 8 xx 8 xx 2)`
⇒ Area (Δ) = 48 cm2
As the sides of the other triangle are also same, so their areas will also be equal.
Area (Rhombus) = Area (Δ) + Area (Δ)
⇒ Area (Rhombus) = 48 + 48 = 96 cm2
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