Find the shaded area in the octagon
1 answer:
See attached graphic.
Triangle ABC is a 45 45 90 triangle.
Side AB = Side BC = hypotenuse * (1 / sq root (2) )
SIde AB = BC = 10 * <span> <span> <span> 0.7071067812 </span> </span> </span>
SIde AB = BC = <span>7.071067812
Area of Triangle ABC = (AB * BC) / 2</span><span>
Area of Triangle ABC = 25
</span><span>Area of Triangle DEF = 25
Line FB = 10
Line FD = </span><span>7.071067812
Area of Rectangle FBDA = </span><span>70.71067812
Total Area of Shaded Area = 25 + 25 + </span><span>70.71067812 =
120.</span><span>71067812
</span>
Triangle ABC is a 45 45 90 triangle.
Side AB = Side BC = hypotenuse * (1 / sq root (2) )
SIde AB = BC = 10 * <span> <span> <span> 0.7071067812 </span> </span> </span>
SIde AB = BC = <span>7.071067812
Area of Triangle ABC = (AB * BC) / 2</span><span>
Area of Triangle ABC = 25
</span><span>Area of Triangle DEF = 25
Line FB = 10
Line FD = </span><span>7.071067812
Area of Rectangle FBDA = </span><span>70.71067812
Total Area of Shaded Area = 25 + 25 + </span><span>70.71067812 =
120.</span><span>71067812
</span>
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Let the equal sides of the isosceles Δ ABC be x.
Given that the perimeter of Δ ABC = 50m.
Therefore, 2x + AC = 50 --- (1)
It is also given that the perimeter of Δ ABD = 40m.
Therefore, x + BD + AD = 40
BD is the median of the Δ ABC. Therefore, D is the midpoint of AC.
So AD = CD.
Or, AD = AC
Therefore,
Multiply both sides by 2.
2x + 2BD + AC = 80
From (1), 2x + AC = 50.
Therefore, 2BD + 50 = 80
2BD = 80 - 50
2BD = 30
BD = 15m.