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The figure DEFH is a parallelogram. a) Find the area of triangle FGH. b) Find the area of parallelogram DEFH. c) What is the sum of the areas of triangle FGH and parallelogram DEFH?

Mathematics

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3 parts
a

8.91 cm2\text{8.91 cm}^2

b

15.84 cm2\text{15.84 cm}^2

c

24.75 cm2\text{24.75 cm}^2

Step-by-step solution

5 steps

Here's the solution for question 6:

Part a· 2 steps

Find the area of triangle FGH

  1. Determine the base of triangle FGH.

    The figure DEFH is a parallelogram, so DH=EF=4.8 cmDH = EF = 4.8 \text{ cm}.
    The total base DG=10.2 cmDG = 10.2 \text{ cm}.
    The base of triangle FGH is HG=DG−DHHG = DG - DH.

    HG=10.2 cm−4.8 cm=5.4 cmHG = 10.2 \text{ cm} - 4.8 \text{ cm} = 5.4 \text{ cm}

    The height of the triangle is 3.3 cm3.3 \text{ cm}.

  2. Calculate the area of triangle FGH.

    The formula for the area of a triangle is 12×base×height\frac{1}{2} \times \text{base} \times \text{height}.

    Area of △FGH=12×HG×height\text{Area of } \triangle FGH = \frac{1}{2} \times HG \times \text{height} Area of △FGH=12×5.4 cm×3.3 cm\text{Area of } \triangle FGH = \frac{1}{2} \times 5.4 \text{ cm} \times 3.3 \text{ cm} Area of △FGH=2.7 cm×3.3 cm\text{Area of } \triangle FGH = 2.7 \text{ cm} \times 3.3 \text{ cm} Area of △FGH=8.91 cm2\text{Area of } \triangle FGH = \boxed{\text{8.91 cm}^2}

Part b

15.84 cm2\text{15.84 cm}^2

Find the area of parallelogram DEFH

  1. Identify the base and height of parallelogram DEFH.

    The base of the parallelogram is DH=4.8 cmDH = 4.8 \text{ cm}.
    The height of the parallelogram is 3.3 cm3.3 \text{ cm}.

  2. Calculate the area of parallelogram DEFH.

    The formula for the area of a parallelogram is base×height\text{base} \times \text{height}.

    Area of parallelogram DEFH=DH×height\text{Area of parallelogram DEFH} = DH \times \text{height} Area of parallelogram DEFH=4.8 cm×3.3 cm\text{Area of parallelogram DEFH} = 4.8 \text{ cm} \times 3.3 \text{ cm} Area of parallelogram DEFH=15.84 cm2\text{Area of parallelogram DEFH} = \boxed{\text{15.84 cm}^2}

Part c

24.75 cm2\text{24.75 cm}^2

What is the sum of the area of triangle and parallelogram DEFH?

  1. Add the area of triangle FGH and the area of parallelogram DEFH.

    Sum of areas=Area of △FGH+Area of parallelogram DEFH\text{Sum of areas} = \text{Area of } \triangle FGH + \text{Area of parallelogram DEFH} Sum of areas=8.91 cm2+15.84 cm2\text{Sum of areas} = 8.91 \text{ cm}^2 + 15.84 \text{ cm}^2 Sum of areas=24.75 cm2\text{Sum of areas} = \boxed{\text{24.75 cm}^2}
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