Question

nate is painting an arrow on the school parking lot. he draws the edges between the following points on the coordinate - plane: (-2,2), (5,2), (5,6), (12,0), (5, - 9), (0, - 2), (-2, - 2). what is the area of the arrow he is painting? enter your answer in the box. square units

Explanation:

Step1: Divide the arrow - shaped figure into a rectangle and two triangles.

The rectangle has vertices (-2,2), (5,2), (5,0), (-2,0). Its length is \(5 - (-2)=7\) and width is \(2-0 = 2\). The area of the rectangle \(A_{1}=l\times w=7\times2 = 14\).

Step2: Calculate the area of the upper - right triangle.

The upper - right triangle has vertices (5,2), (5,6), (12,0). The base \(b_1\) and height \(h_1\) can be found using the distance formula. The base \(b_1\) (horizontal distance) from \(x = 5\) to \(x = 12\) is \(12 - 5=7\), and the height \(h_1\) (vertical distance) from \(y = 0\) to \(y = 6\) is \(6\). The area of a triangle is \(A=\frac{1}{2}bh\), so \(A_{2}=\frac{1}{2}\times7\times4 = 14\).

Step3: Calculate the area of the lower - right triangle.

The lower - right triangle has vertices (5,0), (5, - 2), (12,0). The base \(b_2\) from \(x = 5\) to \(x = 12\) is \(12 - 5 = 7\), and the height \(h_2\) from \(y = 0\) to \(y=-2\) is \(2\). The area of this triangle \(A_{3}=\frac{1}{2}\times7\times2=7\).

Step4: Calculate the total area of the arrow.

The total area \(A = A_{1}+A_{2}+A_{3}=14 + 14+7=35\).

Answer:

35