Area of regular hexagon ABCDEF in the figure below is 72 cm2 .
Find the area of shadow area.
(1) AP : PB = 1 : 1, CQ : QD = 2 : 1
(2) AR : RF = 1 : 2, DS : SE = 1 : 1
Answer
(1) 18 cm2
(2) 10 cm2
Solution
(1) According to the total of ratios is 1 + 1 = 2 and 2+ 1 = 3, the length of one side is set to 6 which is the least common multiple of 2 and 3.
Answer
(1) 18 cm2
(2) 10 cm2
Solution
(1) According to the total of ratios is 1 + 1 = 2 and 2+ 1 = 3, the length of one side is set to 6 which is the least common multiple of 2 and 3.
An auxiliary line is drawn as shown in the figure below.
The area ratio of △GBC and△GPQ is 6 × 6 : (6 + 3) × (6 + 4) = 2 : 5.
Because the area of △GBC is 72/6 = 12 cm2, the area to be found is 12 × (5 - 2)/2 = 18 cm2.
(2) Same as (1), the length of one side is set to 6.
(2) Same as (1), the length of one side is set to 6.
The area ratio of △FHE and △RSD is 6 × 6 : (10 × 12 - 10 × 9) = 6 : 5.
Therefore the area to be found is 12 × 5/6 = 10 cm2.
