This document is a mathematics assessment that tests a student's understanding of shapes and area formulas. It contains 6 questions that assess the student's knowledge of: 1) finding the area of rectangles and squares, 2) calculating the area and perimeter of a given shape, 3) using the triangle area formula, 4) explaining and applying the parallelogram area formula, 5) identifying trapezoids and explaining their area formula, and 6) finding the area of a hexagon by decomposing it into other shapes. The student must show working for calculations, explain geometric concepts, and apply multiple area formulas to different shapes.

1. Real Mathematics: Shapes Assessment
Name: ……………………………………………….
1.
a) Show on the diagram why the area of any square or rectangle can be found using
the formula: 𝐴𝑟𝑒𝑎 = 𝐿𝑒𝑛𝑔𝑡ℎ × 𝑊𝑖𝑑𝑡ℎ
Use the space below the diagram to write any comments which will help people
understand.
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2. b) Use your knowledge of area to find the missing length of the rectangle (on the
left) and the missing length of the square (on the right). Please show your
working out.
h = …………………. cm
x = ………………….. cm
2. Find the area and perimeter of the shape below:
Area = ………………………………. cm²
Perimeter = ……………………………….. cm

3. 3.
a) Can you explain, using a diagram or writing or both, why the area of any triangle
can be found using the formula: 𝐴𝑟𝑒𝑎 =
𝐵𝑎𝑠𝑒 × 𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝐻𝑒𝑖𝑔ℎ𝑡
2
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b) Use the space below to make two different triangles which have an area of
12 cm². You DO NOT have to draw these shapes with a ruler.

4. 4.
a) The formula for the area of a parallelogram is:
𝐴𝑟𝑒𝑎 = 𝐿𝑒𝑛𝑔𝑡ℎ × 𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝐻𝑒𝑖𝑔ℎ𝑡
Explain why we use the perpendicular height and NOT the slanted height.
You can show this using the diagram or by writing or both.
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b) Find the area of the parallelograms below:
Parallelogram 1
Parallelogram 2
Area of Parallelogram 1: ……………………………… cm²
Area of Parallelogram 2: ……………………………… cm²

5. 5.
a) Circle all of the trapezia below.
b) Explain how the picture below helps to show that the formula for the area of a
trapezium is:
𝐴𝑟𝑒𝑎 =
(𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑆𝑖𝑑𝑒 1 + 𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑆𝑖𝑑𝑒 2) × 𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝐻𝑒𝑖𝑔ℎ𝑡
2
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6. 6.
a) Show three different ways that you could split up the hexagon to find its area.
b) By measuring any necessary parts of the hexagon, find its area in millimetres
squared (mm²).
Area of Hexagon = ………………………………mm²