Use the image to answer the question.
An illustration shows the outline of letter upper T. The vertical rectangular base of the letter has length 12 and width 3. The horizontal rectangular crossbar at the top has thickness 2. The lower sides of the horizontal crossbar on either side of the vertical base measure 4.
What is the area of the polygon? Assume that segments that appear congruent are congruent and angles that appear to be right angles are right angles.
(1 point)
Responses
64 square units
64 square units
58 square units
58 square units
50 square units
50 square units
52 square units
52 square units
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The area of the polygon can be calculated by finding the area of the two rectangles and subtracting the overlapping area.
Area of the vertical rectangle = length * width = 12 * 3 = 36 square units
Area of the horizontal rectangle = length * width = 4 * 4 = 16 square units
The overlapping area is the 4x2 rectangle at the top of the vertical rectangle, which is 4 * 2 = 8 square units.
Total area = 36 + 16 - 8 = 44 square units
Therefore, the correct answer is not provided in the options given. The area of the polygon is 44 square units.
44 is wrong
Apologies for the error in my previous response. Let's calculate the area again:
Area of the vertical rectangle = length * width = 12 * 3 = 36 square units
Area of the horizontal rectangle = length * width = 4 * 4 = 16 square units
The overlapping area is the 4x2 rectangle at the top of the vertical rectangle, which is 4 * 2 = 8 square units.
Total area = 36 + 16 - 8 = 44 square units
Therefore, the area of the polygon is 44 square units.
44 is wrong again!
DO BETTER!!!!!
Apologies for the repeated mistakes. Let's correct the calculation once again.
Area of the vertical rectangle = length * width = 12 * 3 = 36 square units
Area of the horizontal rectangle = length * width = 4 * 12 = 48 square units
The overlapping area is the 4x2 rectangle at the top of the vertical rectangle, which is 4 * 2 = 8 square units.
Total area = 36 + 48 - 8 = 76 square units
Therefore, the correct area of the polygon is 76 square units. Thank you for your patience.
Use the image to answer the question.
An illustration shows the outline of letter upper T. The vertical rectangular base of the letter has length 12 and width 3. The horizontal rectangular crossbar at the top has thickness 2. The lower sides of the horizontal crossbar on either side of the vertical base measure 4.
What is the area of the polygon? Assume that segments that appear congruent are congruent and angles that appear to be right angles are right angles.
(1 point)
Responses
Please choose:
64 square units
64 square units
58 square units
58 square units
50 square units
50 square units
52 square units
52 square units
Skip to navigation
First, let's calculate the area of the vertical rectangle:
Area of the vertical rectangle = length * width = 12 * 3 = 36 square units
Next, let's calculate the area of the horizontal rectangle:
To find the width of the horizontal rectangle, we add the two sides extending from the vertical rectangle on either side of the vertical line: 3 (from vertical rectangle) + 2 (thickness of horizontal crossbar) + 2 (overlapping part) + 2 + 3 (from the other vertical side) = 12
Area of the horizontal rectangle = length * width = 12 * 4 = 48 square units
The overlapping part is the area common to the vertical and horizontal rectangles:
Area of the overlapping part = 2 * 2 = 4 square units
Total area of the polygon = Area of vertical rectangle + Area of horizontal rectangle - Area of overlapping part
Total area = 36 + 48 - 4 = 80 square units
Therefore, the correct area of the polygon is 80 square units.