Question

HELP. SUPER EASY MATH PROBLEM. 20 POINTS

Answer 1

The area of the shaded = the area of the sector - the area of the isosceles triangle.

Split the isosceles triangle in half, each of those triangles is a 30-60-90 triangle, where the radius is the hypotenuse.

Ratio of short leg: long leg: hypotenuse= x : x√3 : 2x

Given hypotenuse = radius = 27.8 in

so short leg = 27.8 / 2 = 13.9 in

long leg = 13.9 √3 = 24.1 in

Area of this isosceles triangle = 24.1 x 13.9 = 334.99 in^2

Area of sector = (150 / 360) π r^2

= (150 / 360) (3.14) (27.8)^2

= 0.4 * (3.14) (772.84)

= 970.7 in^2

Area of shaded = 970.7 in^2 - 334.99 in^2 = 635.71 in^2

= 635.7 in^2 (nearest tenth)

Answer:

635.7 in^2

Answer 2

First find the area of the sector of 150 degrees:

150/360 x PI * 27.8^2 = 1011.6452 in^2

Now find the area of the triangle formed by the 150 degrees and the radius 27.8

first find the length of the chord ( the base of the triangle)

c^2 = 27.8^2 + 27.8^2 - 2 * 27.8 * cos(150) = 53.71

now find the height by using half the chord length as the base and using the Pythagorean theorem:

26.855^2 - 27.8^2 = height^2

height = 7.19

The area of the triangle is 1/2 x base x height = 1/2 x 26.855 x 7.1952 = 96.605

multiply by 2 because we made 2 right triangles: 96.54 x 2 = 193.21 square inches.

Now the area of the shaded region is the area of the sector minus the area of the triangle:

1011.6452 - 193.21 = 818.4352

Rounded to nearest tenth = 818.4 in^2