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Year 9 Maths — Areas on the same base

Use the fact that figures on the same base and between the same parallels have equal areas.

Name: ________________________

  1. 1.Two triangles stand on the same base and between the same parallels. One has an area of 25 square centimetres. What is the area of the other, in square centimetres?

  2. 2.Two parallelograms on the same base and between the same parallels always have...

    • a) equal perimeters
    • b) equal diagonals
    • c) equal areas
    • d) the same shape

  3. 3.All four triangles have bases of the same length on the lower line, and three of them have their tips on the upper line. Tap the triangle with the smallest area.

    Write the number of the part.

    1234

  4. 4.A diagonal splits a parallelogram of area 90 square centimetres into two triangles. What is the area of each, in square centimetres?

  5. 5.Two figures stand on the same base and between the same parallels. Sort each quantity by whether it must be the same for both.

    Groups: Must be the same · Need not be the same

    • The length of their base
    • Their shapes
    • Their areas, if both are parallelograms
    • Their perimeters
    • Their heights
    • The lengths of their slanting sides

  6. 6.A parallelogram and a rectangle stand on the same base and between the same pair of parallel lines. The rectangle's area is 48 square centimetres. What is the parallelogram's area, in square centimetres?

  7. 7.Each triangle's base and height are given in centimetres. Match it to its area in square centimetres.

    • base 10, height 6
    • base 8, height 5
    • base 12, height 9
    • base 7, height 4
    • base 14, height 6
    • 54
    • 20
    • 42
    • 14
    • 30

  8. 8.A triangle has a base of 12 cm and a height of 7 cm. What is its area, in square centimetres?

Answer key — Year 9 Maths — Areas on the same base

  1. 1. 25
  2. 2. c) equal areas
  3. 3. 3 — The third triangle
  4. 4. 45
  5. 5. Their heights → Must be the same; The length of their base → Must be the same; Their areas, if both are parallelograms → Must be the same; Their perimeters → Need not be the same; The lengths of their slanting sides → Need not be the same; Their shapes → Need not be the same
  6. 6. 48
  7. 7. base 10, height 6 → 30; base 8, height 5 → 20; base 12, height 9 → 54; base 7, height 4 → 14; base 14, height 6 → 42
  8. 8. 42