WZ = 5.3 km, find the area of the shaded sectors to the nearest tenth. Please help

The area of the shaded sectors is 35.3 square kilometres

Step-by-step explanation: What we have here is a circle with center Z. Two sectors have been formed which are ZVW and ZYX. A careful observation reveals that both sectors are similar. If WY passes through the center Z then WY is a diameter. The same applies to VX, since it also passes through the center, therefore it is a diameter. Both lines intersect at the center, that makes both sectors to have the same radii which is  5.3 km and same applies to the angle subtended at the center of the sector, both angles are opposite angles formed by intersecting lines (opposite angles formed by intersecting lines are equal). On a straight line WY, the sum of angles ∠WZX and ∠YZX equals 180 degrees (Sum of angles on a straight line equals 180). Therefore;

WZX + YZX = 180

108 + YZX = 180

Subtract 180 from both sides of the equation

YZX = 72°

Therefore the area of shaded sector YZX is given as;

Area of a sector = (∅/360) x πr²

Where ∅ is 72, and r is 5.3

Area of sector = (72/360) x 3.14 x 5.3²

Area of sector = 0.2 x 3.14 x 28.09

Area of sector = 17.64

Having in mind that both sectors are similar (the same radii and the same central angle), the area of the shaded sectors shall be equal to 17.64 times 2 and that equals 35.28. (That is approximately 35.3 to the nearest tenth)

The area of the shaded sectors therefore is 35.3 square kilometres (35.3 km²)

Area of the shaded region ≈ 35.3 km²

Step-by-step explanation:

Area of a sector = ∅/360 × πr²

angle on a straight line  = 180°

Therefore,

∠vzw = 180 - 108 = 72°

∠yzx = 180 - 108 = 72°

Area = 72 /360 × 22/7 × 5.3²

Area = 72 /360 × 22/7 × 28.09

Area = 44494.56/2520

Area = 17.656571429

Area = 17.66 km²

The area is one portion of the shaded part , the area of the 2 shaded sector will be

Area of zvw  + Area of zyx

Both area are same . They have same radius and the same angle.

Area of the shaded region = 17.66 + 17.66

Area of the shaded region ≈ 35.3 km²

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step-by-step explanation:

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