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ABCD EFG is a regular heptagon - Edexcel - GCSE Maths - Question 26 - 2022 - Paper 3
Question 26
ABCD EFG is a regular heptagon. The area of triangle ABG is 30 cm² Calculate the length of GB. Give your answer correct to 3 significant figures. You must show all... show full transcript
Worked Solution & Example Answer:ABCD EFG is a regular heptagon - Edexcel - GCSE Maths - Question 26 - 2022 - Paper 3
Step 1
Start process by finding an angle.
Answer
Since ABCDEFG is a regular heptagon, each interior angle can be calculated using the formula: ext{Interior angle} = rac{(n-2) imes 180^ ext{o}}{n} where n is the number of sides. For a heptagon (n = 7): ext{Interior angle} = rac{(7-2) imes 180^ ext{o}}{7} = rac{900^ ext{o}}{7} \\ ext{Interior angle} \\ ext{approximately } = 128.57^ ext{o}
Step 2
Find the length of side of the polygon.
Answer
The area (A) of triangle ABG is given by the formula: A = rac{1}{2} imes a imes b imes ext{sin}( heta) where A = 30 cm², a = GB, b = AB (side length of heptagon), and ( \theta = 128.57^ ext{o} ). Since AB is also a side of the heptagon, ext{AB} = s = rac{ ext{perimeter}}{n} To find the length of one side: s = rac{a + b + c + d + e + f + g}{7}
Step 3
Step 4
For complete process to find GB.
Answer
Continuing with our calculations:
- Calculate the side length (s) of the heptagon: Assuming an arbitrary side length for a regular heptagon or from previous calculations, we approximate:
- Substitute in angle: ext{GB} = rac{60}{7.6 imes ext{sin}(128.57^ ext{o})} \\ ext{Find sin of angle: } \text{sin}(128.57^ ext{o}) ext{ is calculated.}
- Ultimately, we find: