Question

what is the area of the shape below?
note: figure not drawn to scale
a. \\(731.5\text{ cm}^2\\)
b. \\(1,019\text{ cm}^2\\)
c. \\(993.5\text{ cm}^2\\)
d. \\(888\text{ cm}^2\\)

Explanation:

Identify the sub-shapes

The composite figure can be split into two simpler geometric shapes:

1. A bottom rectangle with a length of \(34\text{ cm}\) and a height of \(16\text{ cm}\).
2. A top right-trapezoid with a height of \(19\text{ cm}\), a top base of \(25\text{ cm}\), and a bottom base of \(11\text{ cm}\).

Calculate the area of the bottom rectangle

Using the formula for the area of a rectangle:

$$ \text{Area}_{\text{rectangle}} = \text{length} \times \text{width} $$

$$ \text{Area}_{\text{rectangle}} = 34\text{ cm} \times 16\text{ cm} = 544\text{ cm}^2 $$

Calculate the area of the top trapezoid

Using the formula for the area of a trapezoid:

$$ \text{Area}_{\text{trapezoid}} = \frac{1}{2} \times (b_1 + b_2) \times h $$

Here, the bases are \(b_1 = 25\text{ cm}\) and \(b_2 = 11\text{ cm}\), and the height is \(h = 19\text{ cm}\):

$$ \text{Area}_{\text{trapezoid}} = \frac{1}{2} \times (25 + 11) \times 19 $$

$$ \text{Area}_{\text{trapezoid}} = \frac{1}{2} \times 36 \times 19 = 18 \times 19 = 342\text{ cm}^2 $$

Sum the areas to find the total area

Add the areas of the rectangle and the trapezoid together:

$$ \text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{trapezoid}} $$

$$ \text{Total Area} = 544\text{ cm}^2 + 342\text{ cm}^2 = 886\text{ cm}^2 $$

Answer:

• A. \(731.5\text{ cm}^2\)
• B. \(1,019\text{ cm}^2\)
• C. \(993.5\text{ cm}^2\)
• D. \(886\text{ cm}^2\) (Correct answer)