Mathematics Question and Solution
EG = 3AG
Let AG = 1 unit.
Therefore;
EG = 3 units.
The side length of the regular pentagon is;
AG+EG = 1+3 = 4 units.
AE = 4 units.
It implies, Area Blue is;
0.5*2*4sin108
= 4sin108
= 3.80422606518 square units.
Calculating Area Green.
(DG)² = 3²+4²-2*3*4cos108
DG = 5.6935408899 units.
It implies;
5.6935408899² = 2(GH)²
(GH)² = 0.5(5.6935408899)²
(GH)² = 16.20820393248 square units.
Area Green= ½(GH)²
= 0.5*16.20820393248
= 8.10410196624 square units.
Therefore;
Area Blue ÷ Area Green is;
3.80422606518÷8.10410196624
= 0.4694198174
≈ 0.47 to 2 decimal places.
