Find the area of the polygon in square units.
Width 7 on both ends
Width 15 on bottom part
13 Length
To find the area of the polygon, we need to break it down into rectangles and triangles and then find the area of each individual shape.
The polygon can be divided into two rectangles and two triangles:
1. Rectangle with width 7 and length 13:
Area = width x length = 7 x 13 = 91 square units
2. Rectangle with width 15 and length 7:
Area = width x length = 15 x 7 = 105 square units
3. Triangle with base 7 and height 6 (calculated by subtracting the overlapping area from the width of the top rectangles):
Area = 0.5 x base x height = 0.5 x 7 x 6 = 21 square units
4. Triangle with base 15 and height 6 (calculated by subtracting the overlapping area from the width of the bottom rectangle):
Area = 0.5 x base x height = 0.5 x 15 x 6 = 45 square units
Total area = 91 + 105 + 21 + 45 = 262 square units
Therefore, the area of the polygon is 262 square units.
No shapes in the solution
My apologies for the error in my previous response.
To find the area of the polygon, we can treat it as a trapezoid, with two parallel sides (widths of 7 units) and a bottom base of 15 units.
The formula for the area of a trapezoid is: (1/2) * (sum of the lengths of the two parallel sides) * (height)
In this case, the sum of the lengths of the two parallel sides is (7 + 7) = 14 units. The height of the trapezoid is 13 units.
Plugging these values into the formula:
Area = (1/2) * 14 * 13
Area = 7 * 13
Area = 91 square units
Therefore, the area of the polygon is 91 square units.
No trapezoid
If we consider the polygon as a composite figure consisting of two rectangles and two right triangles, we can calculate the total area by finding the areas of each of these shapes and then adding them together.
1. Area of the rectangle with width 7 and length 13:
Area = 7 * 13 = 91 square units
2. Area of the rectangle with width 15 and length 7:
Area = 15 * 7 = 105 square units
3. Area of the right triangle with base 8 (15 - 7) and height 6: (since the height of the triangle is perpendicular to the base and can be found by taking away the overlapping width)
Area = 0.5 * 8 * 6 = 24 square units
4. Area of the right triangle with base 15 and height 6:
Area = 0.5 * 15 * 6 = 45 square units
Adding the areas of all individual shapes:
Total Area = 91 + 105 + 24 + 45 = 265 square units
Therefore, the area of the polygon is 265 square units.