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4 This figure is composed of a parallelogram and a trapezoid.
What is the area of the figure in square centimeters?

$4$ This figure is composed of a parallelogram and a trapezoid. $\newline$ What is the area of the figure in square centimeters?

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Area of quadrilaterals and triangles: word problems

Full solution

Q.

4

This figure is composed of a parallelogram and a trapezoid.

\newline

What is the area of the figure in square centimeters?

Identify dimensions: Step $1$ : Identify the dimensions of the parallelogram and trapezoid. Assume the parallelogram has a base of $10\,\text{cm}$ and a height of $5\,\text{cm}$ . The trapezoid has bases of $6\,\text{cm}$ and $4\,\text{cm}$ , and a height of $3\,\text{cm}$ .
Calculate parallelogram area: Step $2$ : Calculate the area of the parallelogram using the formula: Area = base $\times$ height. $\newline$ Area of parallelogram = $10\,\text{cm} \times 5\,\text{cm} = 50\,\text{cm}^2$ .
Calculate trapezoid area: Step $3$ : Calculate the area of the trapezoid using the formula: Area = $\frac{1}{2} \times (\text{Base1} + \text{Base2}) \times \text{Height}$ . $\newline$ Area of trapezoid = $\frac{1}{2} \times (6\,\text{cm} + 4\,\text{cm}) \times 3\,\text{cm} = 15\,\text{cm}^2$ .

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