Q1) Find area of fields
? (-4, 4) (0, 4) (-4, 0) (0, 0)
? ((0,0) (0,-3) (3,-3) (3,0)
? (0,0) (3,0) (7,3) (4,7) (use pythagorean theorem) remember the area is squared already)
To find the area of a field, we can use the formula for the area of a parallelogram, which is base multiplied by height. In this case, we can use the distance formula to find the length of the base and the height.
For the first field, the coordinates are (-4, 4), (0, 4), (-4, 0), and (0, 0). The base is the distance between (-4, 4) and (0, 4), which is 4 units. The height is the distance between (-4, 4) and (-4, 0), which is 4 units. Therefore, the area of the first field is 4 units multiplied by 4 units, which equals 16 square units.
For the second field, the coordinates are (0,0), (0,-3), (3,-3), and (3,0). The base is the distance between (0,0) and (3,0), which is 3 units. The height is the distance between (0,0) and (0,-3), which is 3 units. Therefore, the area of the second field is 3 units multiplied by 3 units, which equals 9 square units.
To find the area of the third field, we can use the Pythagorean theorem to find the lengths of the base and height. The coordinates are (0,0), (3,0), (7,3), and (4,7). The base is the distance between (0,0) and (3,0), which is 3 units. The height is the distance between (3,0) and (4,7), which can be found using the distance formula:
- x-coordinate difference: 4 - 3 = 1
- y-coordinate difference: 7 - 0 = 7
Using the Pythagorean theorem, c^2 = a^2 + b^2, we can find the length of the height:
- c^2 = 1^2 + 7^2
- c^2 = 1 + 49
- c^2 = 50
- c ≈ 7.071
Therefore, the height is approximately 7.071 units. The area of the third field is 3 units multiplied by 7 units (rounded to the nearest whole number), which equals 21 square units.