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Shapes and Area Properties
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Shapes and Area Properties
Use the stated shape properties and area formulas. Include square units in your answers and show working where space is provided.
Identify quadrilaterals
1.A quadrilateral has exactly one pair of parallel sides. Which name best fits it?
- Kite
- Trapezium
- Parallelogram
- Rhombus
2.A quadrilateral has two pairs of adjacent equal-length sides. Which name best describes it?
- Kite
- Trapezium
- Parallelogram
- Rectangle
3.Which quadrilateral has both pairs of opposite sides parallel?
- Kite
- Trapezium
- Parallelogram
- Isosceles triangle
Shape properties
4.Match each shape to one defining property.
- Triangle
- Kite
- Trapezium
- Quadrilateral with two pairs of parallel sides
- Rhombus
- Exactly one pair of parallel sides
- Two pairs of parallel sides
- Four equal sides
- Three sides; interior angles total 180°
- Two pairs of adjacent equal sides
5.In a quadrilateral with two pairs of parallel sides, what relationship do opposite sides have in length?
6.In a quadrilateral with two pairs of parallel sides, the opposite angles are .
7.How many lines of symmetry does a typical kite have?
8.The interior angles of a triangle total degrees.
Calculate area
9.A triangle has a base of 14 cm and a perpendicular height of 9 cm. Find its area.
10.A quadrilateral with two pairs of parallel sides has base 11 m and perpendicular height 7 m. Calculate its area.
11.A trapezium has parallel sides of 13 cm and 7 cm, with a perpendicular height of 5 cm. Work out its area.
12.The diagonals of a kite are 15 cm and 8 cm long. Find the kite’s area.
Symmetry
13.How many lines of symmetry does a regular equilateral triangle have?
- 0
- 1
- 3
- 6
14.How many lines of symmetry does a standard kite have?
15.Sketch an isosceles triangle and show all its lines of symmetry as dashed lines.
16.Sketch a kite with two pairs of adjacent equal sides and mark its line of symmetry using a dashed line.
Apply your understanding
17.At a building site, Arjun marks out a triangular concrete panel with a base of 18 m and a perpendicular height of 12 m. What is the panel’s area?
18.At the same building site, Isla checks a kite-shaped decorative panel with diagonals of 14 m and 9 m. Calculate its area.
19.Select every statement that is always true for a quadrilateral with both pairs of opposite sides parallel.
- The diagonals bisect each other
- All four angles are right angles
- Both pairs of opposite sides have equal lengths
- It has exactly four lines of symmetry
- Opposite angles are equal
20.Explain how a quadrilateral with both pairs of opposite sides parallel differs from a trapezium, using the number of pairs of parallel sides in each description.
21.Why must you identify the correct base and perpendicular height before using an area formula for a shape?
4 printable pages
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Page 2
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