Question

find the sum of the measures of the intieior angles of each polygon.
-hexagon
-pentagon
-quadrilateral
-octagon
-16-gon
-27-gon

The key is the sum of the measures. All of these figures have the same total number of degrees in their interior angles. What do you think that is?


Ms Sue, I have a feeling that you were thinking of the sum of the exterior angles of a polygon.
The question dealt with the sum of the interior angles, which if found by the expression 180*(n-2) where n is the number of sides in the polygon.

Answer 1

Find the area of a polygon with the vertices of (-4,5), (-1,5), (4,-3), and (-4,-3).

Answer 2

Find the area of a polygon with the vertices of (-4,5), (-1,5), (4,-3), and (-4,-3).
176
7
44
88

Answer 3

Find the area of a polygon with the vertices of (-4,5), (-1,5), (4,-3), and (-4,-3).
A. 176
B. 7
C. 44
D. 88

Answer 4

One way to do this is to divide the polygon into simpler shapes, such as triangles and rectangles, and then find the area of each shape and add them up.

One possible way to divide the polygon is to draw a horizontal line that passes through the middle of the polygon, from (-4,1) to (4,1). This line divides the polygon into a rectangle and a triangle.

The rectangle has height 4 (the distance between y-coordinates of (-4,5) and (-4,-3)) and width 8 (the distance between x-coordinates of (-4,5) and (4,-3)). Therefore, its area is:

A_rect = 4 * 8 = 32

The triangle is a right triangle with legs of length 6 (the distance between y-coordinates of (-1,5) and (-4,5)) and 8 (the distance between x-coordinates of (-1,5) and (4,-3)). Therefore, its area is:

A_tri = 1/2 * 6 * 8 = 24

The total area of the polygon is the sum of the areas of the rectangle and the triangle:

A_polygon = A_rect + A_tri = 32 + 24 = 56

Therefore, the area of the given polygon is 56 square units.

Answer 5

The correct answer is 56.

Answer 6

The correct answer is C. 44.