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b) Trapezoid with sides 4cm, 6cm, 5cm, 4cm. c) Trapezoid with sides 8m, 4m, 5m, 8m.

Mathematics

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2 parts
b

20 cm2\text{20 cm}^2

c

30 m2\text{30 m}^2

Step-by-step solution

6 steps

here's how to find the area of these trapeziums.

The formula for the area of a trapezium is:

Area=12(a+b)h\text{Area} = \frac{1}{2}(a+b)h

where aa and bb are the lengths of the parallel sides, and hh is the perpendicular height.

Part b· 3 steps

  1. Identify the parallel sides and the perpendicular height.

    From the image, the parallel sides are a=4 cma = 4 \text{ cm} and b=6 cmb = 6 \text{ cm}.
    The perpendicular height h=4 cmh = 4 \text{ cm} (the side perpendicular to the parallel sides).

  2. Substitute the values into the area formula.

    Areab=12(4 cm+6 cm)(4 cm)\text{Area}_b = \frac{1}{2}(4 \text{ cm} + 6 \text{ cm})(4 \text{ cm})

  3. Calculate the area.

    Areab=12(10 cm)(4 cm)\text{Area}_b = \frac{1}{2}(10 \text{ cm})(4 \text{ cm}) Areab=12(40 cm2)\text{Area}_b = \frac{1}{2}(40 \text{ cm}^2) Areab=20 cm2\text{Area}_b = 20 \text{ cm}^2

    The area of trapezium b) is 20 cm2\boxed{\text{20 cm}^2}.

Part c

30 m2\text{30 m}^2

  1. Identify the parallel sides and the perpendicular height.

    From the image, the parallel sides are a=8 ma = 8 \text{ m} and b=4 mb = 4 \text{ m}.
    The perpendicular height h=5 mh = 5 \text{ m} (the internal line segment shown).

  2. Substitute the values into the area formula.

    Areac=12(8 m+4 m)(5 m)\text{Area}_c = \frac{1}{2}(8 \text{ m} + 4 \text{ m})(5 \text{ m})

  3. Calculate the area.

    Areac=12(12 m)(5 m)\text{Area}_c = \frac{1}{2}(12 \text{ m})(5 \text{ m}) Areac=12(60 m2)\text{Area}_c = \frac{1}{2}(60 \text{ m}^2) Areac=30 m2\text{Area}_c = 30 \text{ m}^2

    The area of trapezium c) is 30 m2\boxed{\text{30 m}^2}.

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