Question

What is the area of a rectangle with vertices at (2, 3), (7, 3), (7, 10), and (2, 10)?

a. 44 units2
b. 30 units2
c. 24 units2
d. 35 units2

Answer 1

d 35 units squared. If you would graph it on a piece of graph paper or look at the points one side would be the difference between 10 and 3 and the other side would be the difference between 7 and 2. Then taking those totals multiple them together to get the area

Answer 2

Answer: The correct option is (d) 35 units².

Explanation: We are given to find the area of a rectangle with vertices at the points (2, 3), (7, 3), (7, 10), and (2, 10).

Let A(2, 3), B(7, 3), C(7, 10), and D(2, 10) represents the co-ordinates of the vertices of the given rectangle.

Then, the lengths of the sides AB, BC, CD and DA ca be calculated using distance formula as follows :

`AB=√((7-2)^2+(3-3)^2)=√(25+0)=√(25)=5~\textup{units},\\\\BC=√((7-7)^2+(10-3)^2)=√(0+49)=√(49)=7~\textup{units},\\\\CD=√((2-7)^2+(10-10)^2)=√(25+0)=√(25)=5~\textup{units},\\\\DA=√((2-2)^2+(3-10)^2)=√(0+49)=√(49)=7~\textup{units}.`

So, the area of the given rectangle will be

`Area=AB*BC=5*7=35~\textup{units}^2.`

Thus, (d) is the correct option.