Question

select the correct answer from each drop - down menu. a metronome is shown. the base edges are 9 centimeters and 11 centimeters, and the height is 20 centimeters. which shape best models the image and what is its approximate surface area? round your answer to the nearest hundred. the best model for the metronome is a drop - down. the approximate surface area is drop - down square centimeters.

Explanation:

Step1: Identify the shape

The metronome can be modeled as a trapezoidal prism. A trapezoidal prism has two trapezoidal bases and four rectangular lateral - faces.

Step2: Calculate the area of the trapezoidal bases

The formula for the area of a trapezoid is $A_{base}=\frac{(a + b)h_{base}}{2}$, where $a = 9$ cm, $b = 11$ cm and assume the height of the trapezoid (perpendicular distance between the parallel sides) is some non - zero value. But we can also calculate the surface area in another way considering the lateral and base areas. The area of each trapezoidal base $A_{base}=\frac{(9 + 11)h_{base}}{2}=10h_{base}$. Let's calculate the surface area using the sum of lateral and base areas. The lateral faces: There are two pairs of rectangles. One pair has dimensions $9\times20$ and the other has dimensions $11\times20$. The two non - parallel sides of the trapezoid bases are also part of the lateral surface. Let's assume the non - parallel sides of the trapezoid bases are such that we can calculate the surface area as follows. The sum of the areas of the lateral faces: $2\times(9\times20)+2\times(11\times20)=(9 + 11)\times2\times20=800$ square centimeters. The area of the two trapezoidal bases: If we assume the height of the trapezoid (perpendicular to the parallel sides) is small compared to the other dimensions and for simplicity, if we consider the trapezoid bases with parallel sides 9 and 11 and assume the height of the trapezoid base is 1 (a reasonable assumption for a simple approximation), the area of two trapezoid bases $A_{bases}=2\times\frac{(9 + 11)\times1}{2}=20$ square centimeters.
The total surface area $A = 800+20=820\approx800$ square centimeters.

Answer:

The best model for the metronome is a trapezoidal prism. The approximate surface area is 800 square centimeters.