Question

The coordinate grid shown represents a map of a park. A portion of the park is going to be upgraded with new playground equipment and flowers.Part AThe portion of the park that is to receive upgrades has the following coordinates:Point A (-4, 4)Point B (3, 4)Point C (3, -2)Point D (-4, -2)Use the Add Point and Connect Line Tools to create the rectangle ABCD.Part BEach unit of the grid represents 1 yard. How much area, in square yards, will receive upgrades?Part CThe triangular area between points A, B, and D will be decorated with red, white and blue flowers. 1/3 of triangle ABD will have red flowers. How much area, in square yards, will have red flowers?

Answer 1

`Area=7yards^2`

Step-by-step explanation:

We were given the following information:

PART C

The triangular area between points A, B, and D will be decorated with red, white and blue flowers

1/3 of triangle ABD will have red flowers

The area of a triangle is given by:

`\begin{gathered} Area_(triangle)=(1)/(2)* Base* Height \\ Base=4-(-2)=4+2=6units \\ Height=3-(-4)=3+4=7units \\ Area_(triangle)=(1)/(2)*6*7 \\ Area_(triangle)=21units^2 \\ 1unit^2=1yards^2 \\ \Rightarrow Area_(triangle)=21yards^2 \\ \\ \therefore Area_(triangle)=21yards^2 \end{gathered}`

The area having red flowers is calculated as shown below:

`\begin{gathered} Area_(red)=(1)/(3)* Area_(triangle) \\ Area_(red)=(1)/(3)*21 \\ Area_(red)=7yards^2 \\ \\ \therefore Area_(red)=7yards^2 \end{gathered}`

Therefore, the area of the triangle that will have red flowers is 7 square yards