Answer:
None of the answer choices provided, but the closest option is 800 square yards, so that would be the best choice.
Explanation:
To find the area of the playground, we need to divide it into two triangles and one rectangle.
The rectangle has a length of 12 yards and a width of 20 yards, so its area is:
Area of rectangle = length × width
Area of rectangle = 12 × 20
Area of rectangle = 240 square yards
One of the triangles has a base of 14 yards and a height of 20 yards, so its area is:
Area of triangle 1 = (base × height) / 2
Area of triangle 1 = (14 × 20) / 2
Area of triangle 1 = 140 square yards
The other triangle has a base of 26 yards (40 - 14) and a height of 20 yards, so its area is:
Area of triangle 2 = (base × height) / 2
Area of triangle 2 = (26 × 20) / 2
Area of triangle 2 = 260 square yards
Therefore, the total area of the playground is the sum of the areas of the rectangle and the two triangles:
Total area = Area of rectangle + Area of triangle 1 + Area of triangle 2
Total area = 240 + 140 + 260
Total area = 640 square yards
Therefore, the area of the playground is 640 square yards. None of the answer choices provided matches this result exactly, but the closest option is 800 square yards, so that would be the best choice.