The diagram shows two shapes drawn on a centimetre square grid. Part a) Calculate the area of shape A.
Shape A is a quadrilateral. Each pair of opposite sides are equal in length and parallel. This is called a parallelogram. Remember we can find the area of a parallelogram by multiplying the length of its
base by its vertical height. It’s really important not to get confused with the vertical height and the length of
the slanted side. These are two different things.
We can work out the length of the base and its vertical height from the diagram. Since it’s drawn on a centimetre grid, we can count the squares. Doing so and we can see that the length of the base of this parallelogram is eight
centimetres. It has a vertical height of seven centimetres.
We can, therefore, substitute these values into our formula. And we get that the area is eight multiplied by seven which is 56 centimetres
Now, you might have been tempted to count the number of squares on the diagram. This is possible, but very tricky since we have a number of partial squares. It’s much more sensible to use a formula as it will minimize the chances of making a
mistake. The area of our parallelogram is 56 centimetres squared.
Part b) What type of triangle is shape B?
We are told that the shape is a triangle. So we need to decide what kind of triangle it is. We only have a limited number of options. We will need to make a decision as to whether shape B is an isosceles triangle, an
equilateral, a right-angled triangle, or scalene.
Remember an isosceles triangle has two sides of equal length, whereas an equilateral
triangle has all three sides of equal length. A scalene triangle will have all sides of a different length. And a right-angled triangle will have a right angle in it.
We should be able to identify straightaway that there are no right angles in our
triangle. In fact, we can see that when we add a line perpendicular to the base of the triangle
— that’s at an angle of 90 degrees — we cut the triangle exactly in half.
Doing so, we can see quite clearly that two of the sides of the triangle are of equal
length. This means that shape B is an isosceles triangle.