The area of the shaded polygon is 75 square units.
The shaded polygon can be divided into a rectangle and two right triangles.
Find the dimensions of each shape: From the image, we can measure the following:
Rectangle: base = 10 units, height = 5 units
Triangle 1: base = 5 units, height = 5 units (since it's a right triangle, the height is equal to half the hypotenuse)
Triangle 2: base = 5 units, height = 5 units (similarly to triangle 1)
Calculate the area of each shape:
Rectangle: area = base × height = 10 units × 5 units = 50 square units
Triangle 1: area = (base × height) / 2 = (5 units × 5 units) / 2 = 12.5 square units
Triangle 2: area = (base × height) / 2 = (5 units × 5 units) / 2 = 12.5 square units
Sum the areas of the shapes: Finally, to find the total area of the shaded polygon, add the areas of the rectangle and the two triangles.
Total area = area of rectangle + area of triangle 1 + area of triangle 2
Total area = 50 square units + 12.5 square units + 12.5 square units
Total area = 75 square units