9414 1404 393
Answer:
A. 3.46
Step-by-step explanation:
The side ratios of a 30°-60°-90° triangle are 1 : √3 : 2. You are given the short side GF of this triangle, so its long side is GH = GF·3.
Then the area of ΔGFH is ...
A = 1/2(GF)(GH) = 1/2(4)(4√3) = 8√3 ≈ 13.86 . . . . square units
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Segment GI divides the area of ΔGFH in half, so that ΔGFI is half the above area. Segments GF, FI, IH, GI are all congruent, so segment GJ divides isosceles triangle GFI in half. That is. ΔGJI is half the area of ΔGFI, so is 1/4 the area of GFH.
Area of ΔGJI = (8√3)/4 = 2√3 ≈ 3.46 . . . square units
