Area of Polygons Quick Check
5 of 55 of 5 Items
Question
Use the image to answer the question.
An illustration shows the outline of letter X. The length of each of the four legs is 7, and the width of each is 5.
What is the area of the polygon? Assume that segments that appear congruent are congruent.
(1 point)
Responses
76 square units
76 square units
165 square units
165 square units
140 square units
140 square units
190 square units
To find the area of the polygon, you can break it down into smaller shapes and find the area of each shape separately.
The polygon can be broken down into two rectangles and two triangles. The two rectangles have dimensions 5 x 7, so their total area is 2 * 5 * 7 = 70 square units.
The two triangles can be broken down into right triangles with legs of 5 and 2 (half of 7). The area of each triangle is 1/2 * base * height, so the area of one triangle is 1/2 * 5 * 2 = 5 square units. Since there are two triangles, their total area is 2 * 5 = 10 square units.
Adding the areas of the rectangles and triangles together, the total area of the polygon is 70 + 10 = 80 square units.
Therefore, the correct answer is not listed in the given options. The closest option is 76 square units. But you can calculate it to find the exact area.