9 (a) A diagonal of a rectangle is drawn on a centimetre grid. The sides of the rectangle are on the grid lines. Work out the area of the rectangle. [2 marks] Answer cm^2 One side of a parallelogram is drawn on this centimetre grid. 9 (b) The parallelogram does not have any right angles. Complete the parallelogram so that it has area 24cm^2 [2 marks] __

## Step 1: Problem analysis<br />The problem has two parts. <br />Part (a) asks us to work out the 'area' of a rectangle when a diagonal is drawn. The given rectangle does not have any specific dimensions given, the problem does not provide sufficient information to solve it.<br />Part (b) asks us to complete the parallelogram such that its area is \(24 \mathrm{cm}^2\). Here, no specific dimensions of the parallelogram or the side drawn on the grid has been provided to sketch.<br />Unfortunately, correct solution computations can't be given without exact measurements. But I can explain how to approach these problems and which formulas to use once you have the necessary details.<br /><br />## Step 2: Area calculation<br />The area of a rectangle and parallelogram is calculated in the same way. It's the product of base and height: <br /><br />### $A = Base * Height $<br /><br />This provides the solution for any problem when the base and height are known.<br /><br />## Step 3: Use the right triangle properties (if a diagonal is present in the rectangle):<br />In the case when a diagonal is given, it's highly likely for the rectangle to also form two right triangles. Using this, an indirect way to find the area might be to calculate the length of the each side using the diagonal based on Pythagorean theorem for one of the right triangles, assuming one would know at least the length of the diagonal and one of the other sides.