Diamond

Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area.

Correct result:

S =  285.2 cm2

Solution:

S=2S1 ΔABC:a=17 a=17 u=22 s=(a+a+u)/2=(17+17+22)/2=28 cm S1=s(sa)(sa)(su) S1=28(2817)(2817)(2822)=142.58 cm2 S=2S1=2142.58=285.2 cm2S = 2 S_1 \ \\ \Delta ABC: a=17 \ a=17 \ u=22 \ \\ s = (a+a+u)/2 = (17 + 17 + 22)/2 = 28 \ cm \ \\ S_1 = \sqrt{ s(s-a)(s-a)(s-u)} \ \\ S_1 = \sqrt{ 28\cdot (28-17)(28-17)(28-22)} = 142.58 \ cm^2 \ \\ S = 2 S_1 = 2 \cdot 142.58 = 285.2 \ \text{cm}^2



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