Question

use the drop-down menus to complete the sentences to determine the total area of the figure. click the arrows to choose an answer from each menu. the trapezoid has a height of 3 inches, a shorter base measuring 4.25 inches, and a longer base measuring choose... inches. the total area of the entire figure is 37.75 square. the options for the longer base are 4.25, 3, 4, 6.75. the figure includes a trapezoid, rectangles, and a triangle with dimensions: 4.25 in, 2.75 in, 4 in, 3 in, 2 in, 2.5 in.

Explanation:

Step1: Identify the longer base of the trapezoid

Looking at the figure, the vertical dimension of the rectangle (which is equal to the longer base of the trapezoid) is 4 inches (from the first rectangle's height which is 4 inches, and since the trapezoid is adjacent to it, the longer base should match this length). So the longer base is 4 inches.

Step2: Calculate the area of each shape

• Rectangle 1: Area = length × width = \(4\times2.75 = 11\) square inches.
• Trapezoid: The formula for the area of a trapezoid is \(A=\frac{(b_1 + b_2)h}{2}\), where \(b_1 = 4.25\), \(b_2 = 4\), \(h = 3\). So \(A=\frac{(4.25 + 4)\times3}{2}=\frac{8.25\times3}{2}=\frac{24.75}{2}=12.375\) square inches.
• Rectangle 2: Area = \(3\times2.75 = 8.25\) square inches.
• Triangle: The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, base = 2.5, height = 2. So \(A=\frac{1}{2}\times2.5\times2 = 2.5\) square inches. Wait, no, wait, the triangle has base 2.5 and height 2? Wait, no, looking at the figure, the triangle: base is 2.5, height is 2? Wait, no, the triangle's height is 2 (the dashed line) and base is 2.5? Wait, no, maybe I misread. Wait, the last shape is a triangle with base 2.5 and height 2? Wait, no, let's recalculate. Wait, maybe the second rectangle is 3x2.75? Wait, no, the first rectangle is 4x2.75, the trapezoid, then a rectangle of 3x2.75, then a triangle with base 2.5 and height 2? Wait, no, maybe the correct areas:

Wait, let's re - evaluate:

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Answer:

The longer base of the trapezoid is 4 inches. The total area of the entire figure is 37.75 square inches.