Use the image to answer the question.
An illustration shows the outline of letter upper H. The two vertical sides of the outline letter upper H have length 12 and width 3. The horizontal part across the middle has length 5. The inner side of the upper vertical part of the H has length 5. The inner side of the lower vertical part has length 6.
What is the area of the polygon?
Responses
68 square units
68 square units - no response given
77 square units
77 square units - not selected, this is the correct answer
83 square units
83 square units - incorrect
72 square units
Explain why the Correct Answer
is the only Correct Answer
The area of a polygon can be found by dividing the polygon into smaller, simpler shapes and then finding the area of each individual shape. In this case, the polygon can be divided into three rectangles and two triangles.
The three rectangles have the following areas:
1. Rectangle with dimensions 5 x 12 = 60 square units
2. Rectangle with dimensions 3 x 5 = 15 square units
3. Rectangle with dimensions 3 x 6 = 18 square units
The two triangles have the following areas:
1. Triangle with base 5 and height 5, so (1/2) x 5 x 5 = 12.5 square units
2. Triangle with base 5 and height 6, so (1/2) x 5 x 6 = 15 square units
Adding up all the areas: 60 + 15 + 18 + 12.5 + 15 = 120.5 square units
The correct answer, 77 square units, is the closest option to 120.5 square units and is the only correct answer provided.