Question

What is the area of a polygon with vertices of (–4, 5), (–1, 5), (4, –3), and (–4, –3)?
(1 point)
Responses

176 square units
176 square units

7 square units
7 square units

44 square units
44 square units

88 square units
88 square units

Answer 1

The area of the polygon can be found by splitting it into two triangles and calculating the area of each triangle separately.

Triangle 1: (-4, -3), (-4, 5), (-1, 5)
Base = 3 units, Height = 8 units
Area = (1/2) * base * height
Area = (1/2) * 3 * 8
Area = 12 square units

Triangle 2: (-4, -3), (-1, 5), (4, -3)
Base = 5 units, Height = 7 units
Area = (1/2) * base * height
Area = (1/2) * 5 * 7
Area = 17.5 square units

Total area of the polygon = Area of Triangle 1 + Area of Triangle 2
Total area = 12 + 17.5
Total area = 29.5 square units

Therefore, the area of the polygon is approximately 29.5 square units.