The relationship between the sides MN, MS, and MQ in the given regular heptagon is
The area to be planted with flowers is approximately <u>923.558 m²</u>
The reason the above value is correct is as follows;
The known parameters of the garden are;
The radius of the circle that circumscribes the heptagon, r = 25 m
The area left for the children playground = ΔMSQ
Required;
The area of the garden planted with flowers
Solution:
The area of an heptagon, is;
The interior angle of an heptagon = 128.571°
The length of a side, S, is given as follows;
The area of the heptagon MNSRQPO is therefore;
By sine rule, we have
∠MSQ = 128.571 - 2*23.18 = 82.211
The area of triangle, MSQ, is given as follows;
The area of the of the garden plated with flowers, , is given as follows;
= Area of heptagon MNSRQPO - Area of triangle ΔMSQ
Therefore;
= 1,842.94 - 919.382 ≈ 923.558
The area of the of the garden plated with flowers, ≈ <u>923.558 m²</u>
Learn more about figures circumscribed by a circle here: