Final answer:
The area of the triangular part labeled XYZ, assuming it is a right-angled triangle occupying half of a square's area, is 32 sq ft, which corresponds to answer option C.
Step-by-step explanation:
The question is asking to determine the area of a triangle labeled XYZ, which is a part of a concrete play area marked off into squares, and then into triangles. Although the dimensions of the triangle are not given in the question, knowing that it is a portion of a square and having the options for the areas, we can still answer the question with the provided information.
Let's assume we are dealing with a standard triangle inscribed in a square. The area of a triangle is calculated using the formula:
Area of a Triangle = (Base x Height) / 2
Since the triangle forms part of the square, its base and height would be equal to the side of the square, assuming we are talking about a right-angled triangle (half of the square).
If the square's area is one of the options given, then the area of the triangle would be half of that since a square can be divided into two right-angled triangles. Therefore, if we select option D (which is the highest area given for a square), the area of the triangle would be:
Area of Triangle XYZ = 64 sq ft / 2 = 32 sq ft
This means that the correct answer, given the options, would be C (32 sq ft).