Rhombus ABCD has perimeter 148, and one of its diagonals has length 28. what is the area of ABCD?
Rhombus ABCD has perimeter 148, and one of its diagonals has length 28. what is the area of ABCD?
call one diagonal p and the other diagonal q
by Pythagoras, (sideRHOMBUS)2 = ( half p )2 + ( half q )2
You can do this because
The diagonals of a rhombus intersect at a 90o angle.
The diagonals of a rhombus bisect each other.
372 = 142 + ( half q )2
1369 = 196 + ( half q )2
( half q )2 = 1173
( half q ) = 34.25
q = 68.5
It was given that p = 28
Arhombus = (p • q) / 2
Arhombus = (28 • 68.5) / 2 = 1918 / 2
A = 959
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