Find the area of the shaded region.

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

3 0

1. If we join another radius to the shaded area, we will notice that the triangle has all sides 4 units, making it an equilateral triangle.

2. Equilateral triangle has all angles 60°

Area of 1 sector = 60/360 x π (4)² = 8.38 units²

$\text {Area of equilateral triangle =} \dfrac{\sqrt{3}}{4} \text{(4)}^2 = 6.93 \text{ units}^2$

Area of 1 shaded part = 8.38 - 6.93 = 1.45 units²

Area of all shaded part = 1.45 x 2 = 2.9 units²

Answer: 2.9 units²

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Step-by-step explanation:

We are asked to find x, a missing side in a triangle.

This is a right triangle because there is a small square in the corner representing a 90 degree or right angle. Therefore, we can use right triangle trigonometry. The three main functions are:

sinθ= opposite/hypotenuse
cosθ= adjacent/hypotenuse
tanθ= opposite/adjacent

Examine the triangle. We will use angle S, measuring 54 degrees, for theta. Side QR, measuring x, is opposite angle S. Side QS, measuring 2.3, is the hypotenuse because it is opposite the right angle. Since we have the opposite and hypotenuse, we will use sine.

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We are solving for x, so we must isolate the variable. It is being divided by 2.3 The inverse operation of division is multiplication, so we multiply both sides by 2.3

$2.3* sin (54)= \frac{x}{2.3}*2.3$