Find the area of the shaded portion in the equilateral triangle with sides 6.

Mathematics

1 answer:

LUCKY_DIMON [66]3 years ago

7 0

Triangle is equilateral with sides of 6.
Therefore all angles = 60°
Ht of 30-60-90 is 3sr3 = 5.196
Area of 30-60-90 = 1/2×b×h = 3×5.196
Area = 15.59
Pie slice from each corner = 60/360×pi×r^2, with r = 3
1/6×pi×9 = 4.71 × 3 pie slices = 14.13
So, shaded inner region = area triangle - 3 pie corners = 15.59-14.13
= 1.46

You might be interested in

An athlete runs around a circular track. The track has a diameter of 200 feet. How many laps does she need to take to run a mile

Shtirlitz [24]

First you have to figure out the length of the track:

$2 * \pi * r$

r is the half of the diameter:
200ft : 2 = 100ft

$2* \pi *100ft$ = 200 $\pi$ ≈ 628,31

The athlete has to run ca. 5280ft for one mile:

5280 : 628,31≈8,4

The athlete has to run 8,4 laps

3 0

3 years ago

A box contains plain pencils and pens. A second box contains color pencils and crayons. One item from each box is chosen at rand

pochemuha

Answer:

1/2

Step-by-step explanation:

its 1 out of 2 chances

6 0

3 years ago

Consider the polynomial f(x) = 5x4+ 3x2+ x + 19. How many complex solutions does the polynomial have?

antiseptic1488 [7]

Answer:

there are 4 complex solutions
3 real zeros and 2 complex zeros

Step-by-step explanation:

1. Descarte's rule of signs tells you there are 0 positive real roots and 0 or 2 negative real roots. (for positive x, signs are ++++ so have no changes; for negative x, signs are ++-+, so have 2 changes.) A graph shows no real roots.

2. There are 3 sign changes in the given polynomial, so 3 or 1 positive real roots. When the sign of x is changed, there are 2 sign changes, so 0 or 2 negative real roots. A graph shows 2 negative and one positive real root (for a total of 3), so the remaining 2 roots are complex.