Six figures: two triangles, two rectangles, one square, and one pentagon.
Van perimeter: 41 ft 10 in, Area: 90 sq ft. Flower perimeter: 49 ft, Area: 148 sq ft.
The image shows a sheet of paper with a graph on it. The graph has 10 units on the x-axis and 10 units on the y-axis. There are six figures on the graph: two triangles, two rectangles, one square, and one pentagon.
Figure 1
This figure is a right triangle with vertices at (-2, 7), (2, 3), and (4, 1). The base of the triangle is 6 units long and the height of the triangle is 4 units long.Perimeter:The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter of this triangle is 6 + 4 + 6 = 16 units.
Area: The area of a right triangle is half the product of the base and the height. Therefore, the area of this triangle is (1/2) * 6 * 4 = 12 square units.
Figure 2
This figure is a rectangle with vertices at (-4, 3), (4, 3), (4, 1), and (-4, 1). The length of the rectangle is 8 units and the width of the rectangle is 2 units.
Perimeter:The perimeter of a rectangle is the sum of the lengths of its sides. Therefore, the perimeter of this rectangle is 8 + 2 + 8 + 2 = 20 units.
Area:The area of a rectangle is the product of the length and the width. Therefore, the area of this rectangle is 8 * 2 = 16 square units.
Figure 3
This figure is a square with vertices at (0, 1), (4, 1), (4, 4), and (0, 4). The side length of the square is 4 units.
Perimeter:The perimeter of a square is the sum of the lengths of its sides. Therefore, the perimeter of this square is 4 + 4 + 4 + 4 = 16 units.
Area:The area of a square is the square of the side length. Therefore, the area of this square is 4 * 4 = 16 square units.
Figure 4
This figure is a right triangle with vertices at (-4, 0), (2, 0), and (2, 3). The base of the triangle is 6 units long and the height of the triangle is 3 units long.
Perimeter:The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter of this triangle is 6 + 3 + 6 = 15 units.
Area:The area of a right triangle is half the product of the base and the height. Therefore, the area of this triangle is (1/2) * 6 * 3 = 9 square units.
Figure 5
This figure is a rectangle with vertices at (0, 4), (4, 4), (4, 1), and (0, 1). The length of the rectangle is 4 units and the width of the rectangle is 3 units.
Perimeter:The perimeter of a rectangle is the sum of the lengths of its sides. Therefore, the perimeter of this rectangle is 4 + 3 + 4 + 3 = 14 units.
Area: The area of a rectangle is the product of the length and the width. Therefore, the area of this rectangle is 4 * 3 = 12 square units.
Figure 6
This figure is a pentagon with vertices at (-3, 4), (3, -1), (5, -3), (1, -3), and (-4, 0). The sides of the pentagon are all equal in length, and each side is 5 units long.
Perimeter: The perimeter of a pentagon is the sum of the lengths of its sides. Therefore, the perimeter of this pentagon is 5 + 5 + 5 + 5 + 5 = 25 units.
Area: The area of a pentagon is difficult to calculate without knowing the specific coordinates of the vertices. However, there are a few approximate formulas that can be used. One such formula is:
Area of pentagon =
where s is the side length of the pentagon. Using this formula, the approximate area of this pentagon is 20.08 square units.
Example-2:
The image shows a two-dimensional model of a van and a flower. The dimensions of the van are 14 ft 7 in. by 6 ft 25 in., and the dimensions of the flower are 11 ft 2 in. by 13 ft 4 in.
To calculate the perimeter of each object, we add the lengths of all the sides. The perimeter of the van is 14 ft 7 in. + 6 ft 25 in. + 14 ft 7 in. + 6 ft 25 in. = 41 ft 10 in. The perimeter of the flower is 11 ft 2 in. + 13 ft 4 in. + 11 ft 2 in. + 13 ft 4 in. = 49 ft.
To calculate the area of each object, we multiply the length by the width. The area of the van is 14 ft 7 in. * 6 ft 25 in. = 90 ft^2. The area of the flower is 11 ft 2 in. * 13 ft 4 in. = 148 ft^2.
The perimeter of the van is 41 feet 10 inches, and the perimeter of the flower is 49 feet. The area of the van is 90 square feet, and the area of the flower is 148 square feet.