Little-known property: _the diagonals cut a trapezoid into four triangles of which one opposite pair have equal areas._ In the trapezoid FBCP, these two triangles are FPX and BCX (with X being the point of intersection of the diagonals). So, amazingly, the area of the whole pentagram is the area of its central pentagon plus half the area of the square 🤩
1/ Label the green part as A and B (the 2 big ones) and C ( the 3 small triangles) and Q the intersecting point of EB and CF we have: Area of FPB= Area of FCB (same base,.same height)-------> Area of BQC=15+C 2/ We have: Area of BEC= half of that of the square = 225/2 and area of ECQ=A+B+15 so Area of ECQ= Area of BEC - Area of BQC-------> A+B+15 = 225/2 - 15 - C------>A+B+C= (225/2) - 30 = 82.5 Area of the green region= 82.5 sq cm
I've been staring at this for ten minutes wondering where the hell to even start :) . So far I've got to the square being 15 x 15 = 225, and three white triangle with little green pointy bits in them. Each white triangle has a height of 15, to I've got to 225 - 15 - 7.5x - 7.5y - 7.5z + three little green pointy bits :) . Good job I'm old enough to laugh at myself. The triangles I refer to are CDE, ABE, and BCF. And that's as far as I can get for now, but I suspect I need to use a different method. I'll check the video after the England v South Africa rugby world cup game.
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Ok this was really cool. Damn I haven't used these math skills in so long. I love watching your videos.
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WOW!
Challenging question but explained nicely by u
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Great geometry lesson! I enjoyed to see how labeling is essential.
Little-known property: _the diagonals cut a trapezoid into four triangles of which one opposite pair have equal areas._
In the trapezoid FBCP, these two triangles are FPX and BCX (with X being the point of intersection of the diagonals).
So, amazingly, the area of the whole pentagram is the area of its central pentagon plus half the area of the square 🤩
Thanks for your feedback! Cheers! 😀
You are awesome. Keep it up 👍
Wowzers!!
I calculated the sum angles of a pentagon, then of a 5 star points. Then I was stumped.
Your solution was so elegant!
Excellent!
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nice one...thx
Thank you too!
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I loved your explanations!
Glad you like them! ❤️
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1/ Label the green part as A and B (the 2 big ones) and C ( the 3 small triangles) and Q the intersecting point of EB and CF
we have: Area of FPB= Area of FCB (same base,.same height)-------> Area of BQC=15+C
2/ We have: Area of BEC= half of that of the square = 225/2 and area of ECQ=A+B+15
so Area of ECQ= Area of BEC - Area of BQC-------> A+B+15 = 225/2 - 15 - C------>A+B+C= (225/2) - 30 = 82.5
Area of the green region= 82.5 sq cm
Thanks for sharing! Cheers!
You are awesome. Keep it up 👍
I've been staring at this for ten minutes wondering where the hell to even start :) . So far I've got to the square being 15 x 15 = 225, and three white triangle with little green pointy bits in them. Each white triangle has a height of 15, to I've got to 225 - 15 - 7.5x - 7.5y - 7.5z + three little green pointy bits :) . Good job I'm old enough to laugh at myself. The triangles I refer to are CDE, ABE, and BCF. And that's as far as I can get for now, but I suspect I need to use a different method. I'll check the video after the England v South Africa rugby world cup game.
Boka explanation
Fantastic solution and explanation 👍, thank you teacher 🙏.
You are welcome!
Thanks for your feedback! Cheers! 😀
You are awesome. Keep it up 👍