Question

Use each of the three corresponding base and height pairs to find the area of the triangle. Why is the area the same for each calculation?

Answer 1

The three correct corresponding pairs that gives the same area are;

`\begin{gathered} A=(1)/(2)*10*3.5=17.5cm^2 \\ A=(1)/(2)*5*7=17.5cm^2 \\ A=(1)/(2)*14*2.5=17.5cm^2 \end{gathered}`

The areas are the same in each case because the product of each pair is the same.

Step-by-step explanation:

Given the base and height pairs in the question.

Let us use the corresponding pairs that gives the same area.

Firstly, for the first pair;

`\begin{gathered} A=(1)/(2)*10*3.5=17.5cm^2 \\ A=(1)/(2)*10*7=35cm^2 \\ A=(1)/(2)*10*2.5=12.5cm^2 \end{gathered}`

Secondly, the second pair is;

`\begin{gathered} A=(1)/(2)*5*7=17.5cm^2 \\ A=(1)/(2)*5*3.5=8.75cm^2 \\ A=(1)/(2)*5*2.5=6.25cm^2 \end{gathered}`

Thirdly, the third pair;

`\begin{gathered} A=(1)/(2)*14*3.5=24.5cm^2 \\ A=(1)/(2)*14*7=49cm^2 \\ A=(1)/(2)*14*2.5=17.5cm^2 \end{gathered}`

Therefore, the three correct corresponding pairs that gives the same area are;

`\begin{gathered} A=(1)/(2)*10*3.5=17.5cm^2 \\ A=(1)/(2)*5*7=17.5cm^2 \\ A=(1)/(2)*14*2.5=17.5cm^2 \end{gathered}`

The areas are the same in each case because the product of each pair is the same.