Mathematics, 19.12.2019 05:31 aashna66

Abc is an equilateral triangle with sides equal to 2 cm. bc is extended its own length to d, and e is the midpoint of ab. ed meets ac at f. find the area of the quadrilateral befc in square centimeters in simplest radical form.

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Answer from: lokaranjan5736

$\frac{2\sqrt3}{3}$ cm^2

Step-by-step explanation:

Since $\triangle ABC$ is equilateral triangle, then $\angle A = \pi /3$

So,

$S_{\triangle ABC} = \frac{2 * 2 * sin(\pi /3)}{2} = \frac{2 * 2 * \sqrt{3}/2}{2} = \sqrt{3}$ cm^2

Then we need to find $S_{\triangle AEF}$ which can be computed by finding length_AF.

Let's call x = length_AF.

By Menelao's Theorem,

$\frac{BE*x*CD}{AE*(2-x)*BD} = \frac{1*x*2}{1*(2-x)*4} = 1$

⇒ x = 4/3 cm

Thus,

$S_{\triangle AEF} = \frac{1 * x * sin(\pi /3)}{2} = \frac{1 * 4/3 * \sqrt{3}/2}{2} = 1/\sqrt{3}$ cm^2

To find the area of quadrilateral BEFC , we have to subtract $S_{\triangle AEF}$ from $S_{\triangle ABC}$

Hence,

$S_{BEFC} = S_{\triangle ABC} - S_{\triangle AEF} = \sqrt3 -1/\sqrt3 = \frac{2\sqrt3}{3}$ cm^2

Answer from: Quest

step-by-step explanation:

a. since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since 2010 0 1 2 3 4 5

profits made in 1000's 39 84 111 120 111 84

we find that profit gradually increases form 2010 to 2013 upto 120, then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a. since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

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Abc is an equilateral triangle with sides equal to 2 cm. bc is extended its own length to d, and e i...