Question

Triangle DEF is a right triangle with point F at the origin. Segment DE has endpoints located at D(8, 0) and E(0, −2). What is the area of triangle DEF?Options-8 square units18 square units10 square units16 square units

Answer 1

Step-by-step explanation:

Given;

We are given the triangle DEF on the coordinate plane. The coordinates are also given as follows;

`F=(0,0),D=(8,0),E=(0,-2)`

Required;

We are required to calculate the area of triangle DEF.

Step-by-step solution;

We shall begin by drawing up the triangle with the coordinates given, on a graph page;

Observe that the points DEF has been appropriately labeled. The length of side FD is 8 units (that is, from point 0 to 8), the length of side FE is 2 units.

We now have the base (side FE) and the vertical height (side FD), we can calculate the area of the triangle using the formula;

`\begin{gathered} Area\text{ }of\text{ }a\text{ }triangle: \\ \\ Area=(1)/(2)bh \end{gathered}`

Where the variables are;

`\begin{gathered} base=2 \\ height=8 \end{gathered}`

The area therefore is;

`\begin{gathered} Area=(1)/(2)*2*8 \\ \\ Area=8 \end{gathered}`

We now have;

ANSWER:

Area = 8 square units

The first option is the correct answer