Sec 1 Maths · Perimeter and area

Triangles, parallelograms and trapeziums questions with answers

Practice questions on triangles, parallelograms and trapeziums, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

In the diagram, $ABC$ is a triangle. The dashed line is perpendicular to $AB$ . Find the area of triangle $ABC$ .

Step 1 of 1

Use the base AB and the perpendicular height (dashed), not the slant side AC

\text{Area of } \triangle ABC = \dfrac{1}{2} \times \text{base} \times \text{height}

= \dfrac{1}{2} \times 30 \times 15

= 225

cm²

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Questions

Question 1Area of a triangle
In the diagram, $ABC$ is a triangle. The dashed line is perpendicular to $AB$ produced. Find the area of triangle $ABC$ .
Show the worked solution
1. Step 1: Use the base AB and the perpendicular height (dashed), not the slant side AC $\text{Area of } \triangle ABC = \dfrac{1}{2} \times \text{base} \times \text{height}$ $= \dfrac{1}{2} \times 18 \times 9$ $= 81$ cm²
Question 2Area of a parallelogram
In the diagram, $ABCD$ is a parallelogram. The dashed line is perpendicular to $AB$ . Find the area of $ABCD$ .
Show the worked solution
1. Step 1: Use the base AB and the perpendicular height (dashed), not the slant side AD $\text{Area of } ABCD = \text{base} \times \text{height}$ $= 22 \times 12$ $= 264$ cm²
Question 3Area of a trapezium
In the diagram, $ABCD$ is a trapezium with $AB$ parallel to $DC$ . The dashed line is perpendicular to $AB$ . Find the area of $ABCD$ .
Show the worked solution
1. Step 1: Add the two PARALLEL sides, then use the perpendicular height (dashed) $\text{Area of } ABCD = \dfrac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$ $= \dfrac{1}{2} \times (8 + 36) \times 15$ $= 330$ cm²
Question 4Perimeter
The diagram shows the parallelogram $ABCD$ . Find its perimeter.
Show the worked solution
1. Step 1: Opposite sides of a parallelogram are equal $DC = AB$ $\phantom{DC} = 27$ m $BC = AD$ $\phantom{BC} = 29$ m
2. Step 2: Add the lengths of the sides (the height is not a side) $\text{Perimeter} = 27 + 29 + 27 + 29$ $= 112$ m
Question 5A missing length from the area
The area of triangle $ABC$ is $72$ cm². Find the value of $h$ .
Show the worked solution
1. Step 1: Area = ½ × base × height: put in what you know $\dfrac{1}{2} \times 16 \times h = 72$
2. Step 2: Solve $8h = 72$ $h = \dfrac{72}{8}$ $h = 9$
Question 6Two heights, one area
In the diagram, $ABCD$ is a parallelogram. The dashed lines are perpendicular to $AB$ and to $AD$ . Find the value of $x$ .
Show the worked solution
1. Step 1: Find the area using base AB and the height to AB $\text{Area} = 20 \times 12$ $= 240$ m²
2. Step 2: The same area with base AD and the height to AD, x $15x = 240$ $x = \dfrac{240}{15}$ $x = 16$

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Worked example

In the diagram,

ABC

is a triangle. The dashed line is perpendicular to

AB

. Find the area of triangle

ABC

Step 1 of 1

Use the base AB and the perpendicular height (dashed), not the slant side AC

\text{Area of } \triangle ABC = \dfrac{1}{2} \times \text{base} \times \text{height}

= \dfrac{1}{2} \times 30 \times 15

= 225

cm²

Questions

Question 1Area of a triangle

In the diagram, $ABC$ is a triangle. The dashed line is perpendicular to $AB$ produced. Find the area of triangle $ABC$ .

Show the worked solution

Step 1: Use the base AB and the perpendicular height (dashed), not the slant side AC $\text{Area of } \triangle ABC = \dfrac{1}{2} \times \text{base} \times \text{height}$ $= \dfrac{1}{2} \times 18 \times 9$ $= 81$ cm²

Question 2Area of a parallelogram

In the diagram, $ABCD$ is a parallelogram. The dashed line is perpendicular to $AB$ . Find the area of $ABCD$ .

Show the worked solution

Step 1: Use the base AB and the perpendicular height (dashed), not the slant side AD $\text{Area of } ABCD = \text{base} \times \text{height}$ $= 22 \times 12$ $= 264$ cm²

Question 3Area of a trapezium

In the diagram, $ABCD$ is a trapezium with $AB$ parallel to $DC$ . The dashed line is perpendicular to $AB$ . Find the area of $ABCD$ .

Show the worked solution

Step 1: Add the two PARALLEL sides, then use the perpendicular height (dashed) $\text{Area of } ABCD = \dfrac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$ $= \dfrac{1}{2} \times (8 + 36) \times 15$ $= 330$ cm²

Question 4Perimeter

The diagram shows the parallelogram $ABCD$ . Find its perimeter.

Show the worked solution

Step 1: Opposite sides of a parallelogram are equal $DC = AB$ $\phantom{DC} = 27$ m $BC = AD$ $\phantom{BC} = 29$ m
Step 2: Add the lengths of the sides (the height is not a side) $\text{Perimeter} = 27 + 29 + 27 + 29$ $= 112$ m

Question 5A missing length from the area

The area of triangle $ABC$ is $72$ cm². Find the value of $h$ .

Show the worked solution

Step 1: Area = ½ × base × height: put in what you know $\dfrac{1}{2} \times 16 \times h = 72$
Step 2: Solve $8h = 72$ $h = \dfrac{72}{8}$ $h = 9$

Question 6Two heights, one area

In the diagram, $ABCD$ is a parallelogram. The dashed lines are perpendicular to $AB$ and to $AD$ . Find the value of $x$ .

Show the worked solution

Step 1: Find the area using base AB and the height to AB $\text{Area} = 20 \times 12$ $= 240$ m²
Step 2: The same area with base AD and the height to AD, x $15x = 240$ $x = \dfrac{240}{15}$ $x = 16$