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# Find the area of a rhombus one side of which measures 20

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Manager
Joined: 24 Jan 2005
Posts: 217
Location: Boston
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Find the area of a rhombus one side of which measures 20 [#permalink]  23 Mar 2005, 14:31
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Find the area of a rhombus one side of which measures 20 units and one diagonal 24 units

(a) 260 sq units
(b) 280 sq units
(c) 342 sq units
(d) 384 sq units
(e) 424 sq units
Senior Manager
Joined: 15 Mar 2005
Posts: 419
Location: Phoenix
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Re: PS Area of a rhombus [#permalink]  23 Mar 2005, 15:33
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(D) 384.

Consider 1 triangle formed when both diagonals are drawn.

side ^ 2 = (1/2 diagonal 1)^2 + (1/2 diagonal 2)^2
400 = 144 + (1/2 diag 2) ^2
=> diag 2 = 32.

diag 1 = 24.

Area = 24 x 16 = 384.
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Manager
Joined: 15 Feb 2005
Posts: 246
Location: Rockville
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ar of rhombus ==> 1/2(diag1*diag2)
point of intersection makes right angles
diag 1= 24
diag 2=32
ar == 1/2(32*24)
Manager
Joined: 25 Oct 2004
Posts: 249
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D................

(Side)^2= ((diagonal 1)/2)^2+((diagonal 2)/2)^2
(20^2= (24/2)^2 + ((diag 2)/2)^2

solving diagonal 2 =32
Area =1/2*32*24
VP
Joined: 30 Sep 2004
Posts: 1488
Location: Germany
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the rhombus satisfies p^2+q^2=4a^2 where p is diag1, q is diag2 and a is on side => insert the numbers => solve for q or p => p or q is 32 => area of a rhombus = 1/2 * p * q => 1/2 * 32 * 24 = 384
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