What is the perimeter of a regular heptagon if one side measures 3 inches

1 answer:

7 0

What's a regular heptagon? "Hept-" means seven, so a "heptagon" is a seven-sided shape. A "regular" figure's sides are all the same length. So, each of the 7 sides are the same length.

Remember, perimeter is the sum of the lengths of all the sides in a polygon. We know one side measures three inches, so each of the others must also measure 3 inches. 3+3+3+3+3+3+3=3*7=21 inches.

Answer: 21 inches

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Triangle DEF has vertices D(0,0), E(7,0), and F(3,7).

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(3, 1.7)

Step-by-step explanation:

The point at which the vertices of a triangle meet is known as the orthocenter of the triangle. The orthocenter passes through the vertex of the triangle and is perpendicular to the opposite sides.

Two lines are perpendicular if the product of their slopes is -1.

The slope of the line joining D(0,0), F(3,7) is:

$m_1=\frac{7-0}{3-0}=\frac{7}{3}$

The slope of the line perpendicular to the line joining D and F is -3/7. The orthocenter is perpendicular to the line joining D and F and passes through vertex E(7, 0). The equation is hence:

$y-y_1=m(x-x_1)\\\\y-0=-\frac{3}{7} (x-7)\\\\y=-\frac{3}{7}x+3 \ .\ .\ .\ (1)$

The slope of the line joining E(7,0), and F(3,7). is:

$m_1=\frac{7-0}{3-7}=-\frac{7}{4}$

The slope of the line perpendicular to the line joining E and F is 4/7. The orthocenter is perpendicular to the line joining E and F and passes through vertex D(0, 0). The equation is hence:

$y-y_1=m(x-x_1)\\\\y-0=\frac{4}{7} (x-0)\\\\y=\frac{4}{7} x\ .\ .\ .\ (2)$