Shape and Space 4

3 marks · Normal

In a quadrilateral ABCD, angles ABC and CDA are right angles. AB = 9 cm, BC = 5 cm, and CD = 7 cm. Describe how you would calculate the area of quadrilateral ABCD.

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Also accept: Splitting into two right-angled triangles

Common mistakes: Just multiplying two adjacent sides; Not accounting for all areas or the actual shape

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Identifies need to split the quadrilateral into two triangles (or a rectangle and triangle)

M2 · 1 mark · Correctly states how to find the area of each part (uses appropriate area formulae for triangle and rectangle)

A1 · 1 mark · Correctly adds the areas to state or give a complete formula for the total area (follow-through)

Worked solution

I would split quadrilateral ABCD into two right-angled triangles, using AC as a diagonal. Calculate the area of triangle ABC (right-angled at B) as (1/2) × AB × BC, and triangle CDA (right-angled at D) as (1/2) × CD × AD. To find AD, use Pythagoras' theorem if the length is not given. Then add the two triangle areas to get the total area of the quadrilateral.