Find the area of the shaded portion in the equilateral triangle with sides 6. Show all work for full credit. (Hint: Assume that the central point of each arc is its corresponding vertex.)

Area of the shaded region is 1.45 square units.

Step-by-step explanation:

Area of the shaded region = Area of the triangle - Area of three sectors of a circle formed inside the triangle

Area of the given equilateral triangle =

=

= 9√3

= 15.59 square units

Area of one sector of a circle =

=

= 1.5π

= 4.712 square units

Area of the shaded region = [15.59 - (3 × 4.712)]

= 15.59 - 14.14

= 1.45 square units

Therefore, area of the shaded region is 1.45 square units

5050

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d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it