Question

(1a) Clare drew a dashed line as shown in the diagram. She said the thattwo resulting shapes have the same area. Do you agree? *

Answer 1

The area of a rectangle is given by the formula:

`A=b* h`

Where b is the length of the base and h is the height of the rectangle.

The area of a triangle is given by the formula:

`A=(b* h)/(2)`

Where b is the length of the base of the triangle and h is its height.

The resulting shape on the right is a rectangle, whose base is 2 and its height is 4, then the area of this part of the shape is:

`\begin{gathered} A=b* h \\ A=2*4=8 \end{gathered}`

The area of the triangle resulting on the left side is:

`\begin{gathered} A=(b* h)/(2) \\ A=(4*4)/(2)=(16)/(2)=8 \end{gathered}`

Since the area of both shapes is 8, Clare is right.