How is the formula for finding the sum of interior angle measures of polygons dervived

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

8 0

Step-by-step explanation:

Draw lines from one vertex to the other vertices, splitting the polygon into triangles. If the polygon has n sides, there will be n−2 triangles. Each triangle's angles add up to 180°. So the sum of all the interior angles is:

S = (n−2) 180°

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Area of a triangle with verticals of (-4,1),(-7,5),(0,1)

Lynna [10]

Answer:

$8 ft^2$

Step-by-step explanation:

I assume that the three points given are the vertices of the triangle. So the three points are:

A (-4,1)

B (-7,5)

C (0,1)

The area of a triangle is given by:

$A=\frac{1}{2}bh$

where b is the base and h is the height.

Here we can take as follows:

- We can take the base to be the side AC, so that its length is equal to the distance between the two points:

$AC=\sqrt{(0-(-4))^2+(1-1)^2}=4$

- The height of the triangle is therefore the perpendicular distance between AC and point B. This is equivalent the difference in the x-coordinate between any point on AC and B, so:

$h=(5-1)=4 ft$