Finding the Area of a Garden
Use the image to complete the activity.
1. A square garden has the end points listed below. Plot and label these points on the grid: (1 point)
a. A (-7, 6)
b. B (-2, -6)
c. C (10, -1)
d. D (5, 11)
2. Connect the points to create Square ABCD. (1 point)
3. SHOW YOUR WORK: Use the Pythagorean Theorem to find the side length, s, of Square ABCD in feet. (3 points)
s = ________feet
4. SHOW YOUR WORK: Use the area formula, A = s2, to find the area of Square ABCD. (1 point)
A = ________feet2
1. The points A (-7, 6), B (-2, -6), C (10, -1), and D (5, 11) are plotted on the grid as shown.
2. Connect the points A, B, C, and D to create Square ABCD.
3. To find the side length of Square ABCD in feet, we can use the distance formula or the Pythagorean Theorem.
Using the distance formula, we have:
AB = √((-2 - (-7))^2 + (-6 - 6)^2) = √(5^2 + 12^2) = √(25 + 144) = √169 = 13 feet
Therefore, the side length of Square ABCD is 13 feet.
4. To find the area of Square ABCD, we can use the area formula A = s^2, where s is the side length of the square.
A = 13^2 = 169 square feet
Therefore, the area of Square ABCD is 169 square feet.
. SHOW YOUR WORK: Use the Pythagorean Theorem to find the side length, s, of Square ABCD in feet.
To find the side length of Square ABCD using the Pythagorean Theorem, we need to find the distance between two of the points on a side of the square.
Let's find the distance between points A (-7, 6) and B (-2, -6):
The horizontal distance between the points is 7 - (-2) = 9 units.
The vertical distance between the points is 6 - (-6) = 12 units.
Using the Pythagorean Theorem, we can find the distance between the points:
Distance = √(horizontal distance^2 + vertical distance^2)
Distance = √(9^2 + 12^2)
Distance = √(81 + 144)
Distance = √(225)
Distance = 15 units.
Therefore, the side length (s) of Square ABCD is 15 units (or feet).
To find the area of the square garden, we need to follow the given steps:
1. Plot and label the points A (-7, 6), B (-2, -6), C (10, -1), and D (5, 11) on the grid. Make sure to use the x-axis for the horizontal coordinates and the y-axis for the vertical coordinates.
2. Connect the points A, B, C, and D to create Square ABCD. This will form the sides of the square.
3. Now, we need to find the side length of Square ABCD using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
To apply the Pythagorean Theorem, we have two sides: AB and BC. The third side, AC, is the diagonal of the square. We can find the length of AB and BC using the given coordinates and the distance formula:
AB = √((x2 - x1)^2 + (y2 - y1)^2)
= √((-2 - (-7))^2 + (-6 - 6)^2)
= √((-2 + 7)^2 + (-6 + 6)^2)
= √(5^2 + 0^2)
= √(25)
= 5 feet (approx.)
BC = √((x2 - x1)^2 + (y2 - y1)^2)
= √((10 - (-2))^2 + (-1 - (-6))^2)
= √((10 + 2)^2 + (-1 + 6)^2)
= √(12^2 + 5^2)
= √(144 + 25)
= √(169)
= 13 feet (approx.)
Since AB and BC are both sides of the square, s is equal to either AB or BC. Therefore, s = 5 feet (approx.)
4. Finally, use the area formula A = s^2 to find the area of Square ABCD:
A = 5^2
= 25 square feet