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.
Find the area of a polygon with the vertices of (-4,5), (-1,5), (4,-3), and (-4,-3).
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.
Find the area of a polygon with the vertices of (-4,5), (-1,5), (4,-3), and (-4,-3).
176
7
44
88
The correct answer is 56.
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
The correct answer is C. 44.
To find the sum of the measures of the interior angles of each polygon, you can use the formula 180 * (n - 2), where n represents the number of sides in the polygon.
For the given polygons:
- Hexagon: n = 6, so the sum of the interior angles = 180 * (6 - 2) = 180 * 4 = 720 degrees.
- Pentagon: n = 5, so the sum of the interior angles = 180 * (5 - 2) = 180 * 3 = 540 degrees.
- Quadrilateral: n = 4, so the sum of the interior angles = 180 * (4 - 2) = 180 * 2 = 360 degrees.
- Octagon: n = 8, so the sum of the interior angles = 180 * (8 - 2) = 180 * 6 = 1080 degrees.
- 16-gon: n = 16, so the sum of the interior angles = 180 * (16 - 2) = 180 * 14 = 2520 degrees.
- 27-gon: n = 27, so the sum of the interior angles = 180 * (27 - 2) = 180 * 25 = 4500 degrees.
Therefore, the sum of the measures of the interior angles for each polygon is as follows:
- Hexagon: 720 degrees
- Pentagon: 540 degrees
- Quadrilateral: 360 degrees
- Octagon: 1080 degrees
- 16-gon: 2520 degrees
- 27-gon: 4500 degrees.