Question

finding the perimeter of a kite in the coordinate plane
a sandbox is shaped like a kite. a planner would like to replace the wooden border around the sandbox. how many feet of wood does he need? round up to the nearest whole number
feet

Explanation:

1. Assume the vertices of the kite - shaped sandbox in the coordinate - plane have coordinates \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\), and \((x_4,y_4)\). The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

• However, since we don't have the exact coordinates given in the problem description, let's assume we can count the grid - squares. Each grid - square represents 1 unit (1 foot in this context).
• Suppose the lengths of the four sides of the kite are \(a\), \(b\), \(c\), and \(d\).
• By counting the horizontal and vertical displacements between the vertices of the kite and using the Pythagorean theorem (for non - horizontal and non - vertical sides), if we have a side with horizontal displacement \(x\) and vertical displacement \(y\), the length of the side \(l=\sqrt{x^{2}+y^{2}}\).
• Let's assume we find the lengths of the four sides by counting and applying the Pythagorean theorem:
• For example, if one side has a horizontal displacement of 3 units and a vertical displacement of 4 units, its length \(l_1=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\) feet.
• After finding the lengths of all four sides \(a\), \(b\), \(c\), and \(d\) of the kite, the perimeter \(P=a + b + c + d\).
• Let's assume we count and calculate the lengths of the sides and get \(a = 5\), \(b = 5\), \(c = 7\), \(d = 7\).

1. Calculate the perimeter:

• \(P=a + b + c + d\).
• Substitute the values: \(P=5 + 5+7 + 7\).
• \(P = 24\) feet.

Step1: Identify the method

Use the distance formula (or count grid - squares and Pythagorean theorem) to find side lengths.

Step2: Calculate side lengths

Count grid - squares and apply \(l=\sqrt{x^{2}+y^{2}}\) for non - horizontal/vertical sides.

Step3: Calculate perimeter

Sum up the lengths of all four sides \(P=a + b + c + d\).

Answer:

24