Question

question 5(multiple choice worth 1 points)
(08.04 mc)
if w = 10 units, x = 5 units, and y = 6 units, what is the surface area of the figure? round your answer to the nearest tenth
o 456.2 units²
o 256.2 units²
o 400 units²
o 656.2 units²

Explanation:

Step1: Calculate the area of the parallelogram - like faces

The formula for the area of a parallelogram is \(A = base\times height\). Here, the base is \(w = 10\) and the height is \(x = 5\).

$$A_{parallelogram}= 2\times(w\times x)=2\times(10\times5) = 100$$

Step2: Calculate the area of the triangular faces

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). The base is \(x = 5\) and the height is \(y = 6\). There are \(4\) triangular faces.

$$A_{triangle}=4\times(\frac{1}{2}\times x\times y)=4\times(\frac{1}{2}\times5\times6)=60$$

Step3: Calculate the area of the hexagonal face

The formula for the area of a regular hexagon with side - length \(s\) (here \(s = w=10\)) is \(A = \frac{3\sqrt{3}}{2}s^{2}\).

$$A_{hexagon}=\frac{3\sqrt{3}}{2}\times10^{2}=\frac{3\sqrt{3}}{2}\times100 = 150\sqrt{3}\approx259.8$$

Step4: Calculate the total surface area

$$A = A_{parallelogram}+A_{triangle}+A_{hexagon}=100 + 60+259.8=419.8\approx420$$

Answer:

C. 400 units²