Answer:
Andrea Area = 4 x 10.7 + 20 = 62.8cm
Where Lin would be slightly smaller due to inequality Lin Area = 60cm
Therefore Andréa's area = 62.8cm is more precise to 2 and 3 significant figures.
Step-by-step explanation:
Lin and Andre used different methods to find the area of a regular hexagon with 5 cm sides. Lin decomposed the hexagon into six identical triangles. Andre decomposed the hexagon into a rectangle and two triangles. Find the area of the hexagon using each person’s method. Show your reasoning.
Lins Hexagon = 6 triangles
Formula see picture why we say 4 x isosceles for Andre
You will notice that a rectangle is formed using 2 isosceles triangles and 2 equilateral triangles. So as these reflect we show a formula of 4 isosceles.
Lin = 6 x TA
Andre = 4 x isosceles Area + 2 x Equilateral
Therefore if a side measures 5cm
Lin = 1/2 x 5 x 2.5 = 10cm
6 triangles = 10 x 6 = 60cm
If Andres hexagon is also 5cm sides = 10cm area
Then 2x 10 = 20
and isosceles = 5cm edges
The rest is found Pythagoras
5^2 - 2.5^2 = 4.33^2
4.33 x 2 = 8.66 as we halved the triangle and the sq rt is already squared as 4.33 to find c.
however area = 1/2 x 4.3 x 2.5 = 5.35 each half
= 10.7 per isosceles
Area = 4 x 10.7 + 20 = 62.8cm
therefore Andréa's area = 62.8cm is more precise to 2.8cm
