Areas of Triangles, Parallelograms and Trapeziums

If the area is 50cm2 and the base 20cm, what is the perpendicular height?

Triangles XYZ and PQR are drawn on a square grid. What fraction of the area of triangle XYZ is the area of triangle PQR?

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{1}{4}$

• $\frac{1}{5}$

Each square in the figure is 1 unit by 1 unit. What is the area of triangle ABM (in square units)?

Bob has a garden in the shape of a trapezium. If it costs £15.22 per m2 of turf, how much will it cost to turf his garden?

Answer explanation

Did you include the units of your answer?

Which of the following shaded regions has an area different from the other shaded regions?

• A

• B

• C

• D

• E

The area of this trapezium is 51cm². Determine a.

Triangle PQU has a right angle at U. The points R, S and T divide the side QU into quarters. Which of the following statements about the areas of the triangles PQR, PRS, PST, PTU is true?

• All have the same area

• ΔPQR is biggest

• ΔPRS is biggest

• ΔPST is biggest

• ΔPTU is biggest

If AB=9cm, AC=6cm, D is a point such that CD is perpendicular to AB and CD=4cm, E is a point such that AC is perpendicular to BE, then what is the length of BE?

In the diagram, AB=AD=AE and BD=10cm. Determine the length BE, in cm, leaving your answer as a fraction.
Give your answer as an improper fraction.

For example $\frac{8}{3}$  would be entered as 8/3

The diagram shows three congruent regular hexagons. Some diagonals have been drawn, and some regions then shaded. The total shaded areas of the hexagons are X, Y, Z as shown. Which of the following statements is true?

• X,Y and Z are all the same

• Y and Z are equal, but X is different

• X and Z are equal, but Y is different

• X and Y are equal, but Z is different

• X,Y,Z are all different