Question

Question In this polygon, all angles are right angles. What is the area of this polygon? Enter your answer in the box. ft² Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle. The left side of the figure is 18 ft, the bottom side of the figure is 21 ft, the right side of the figure is 8 ft, and the top part of the horizontal rectangle to the right of the vertical rectangle is 12 ft.

Answer 1

Answer:To find the area of the polygon, we need to split it into smaller rectangles and then add up their areas.

Step-by-step explanation:First, we can split the L-shaped polygon into two rectangles: one with dimensions 18 ft by 12 ft (top part of the L) and the other with dimensions 21 ft by 8 ft (bottom part of the L).

The area of the first rectangle is:

18 ft x 12 ft = 216 ft²

The area of the second rectangle is:

21 ft x 8 ft = 168 ft²

To find the total area, we add up the areas of these two rectangles:

Total area = 216 ft² + 168 ft² = 384 ft²

Therefore, the area of the polygon is 384 ft².

Answer 2

• 258 ft² (first attachment)
• 282 ft² (second attachment)

Explanation:

You want the area of an L-shaped rectilinear figure with overall dimensions of 18 ft high and 21 ft wide, and a cutout that is 12 ft wide. The dimension of the "right side of the figure" is given as 8 ft.

Difference of areas

The area of such a figure can be found as the difference between the overall area and the area of the rectangle cutout at upper right. The overall area is ...

A = LW

A = (18 ft)(21 ft) = 378 ft²

Missing corner

If the lower right-side dimension is 8 ft, as in the first attachment, then the rectangle cutout is 10 ft by 12 ft, for an area of ...

cutout = (10 ft)(12 ft) = 120 ft²

The area of the L-shaped figure in the first attachment is ...

378 ft² -120 ft² = 258 ft² . . . . . . area of L-shape (first attachment)

The problem statement is ambiguous as to which right-side dimension is 8 ft. If that is the vertical dimension of the right side of the "vertical rectangle", then the dimensions are those of the second attachment. The cutout area is 8 ft by 12 ft, or 96 ft².

This L-shaped area is ...

378 ft² -96 ft² = 282 ft² . . . . . . . area of L-shape (second attachment)