Areas De Figuras Planas

Explanation
To calculate the number of square tiles needed to tile a rectangular surface, we need to find the area of the surface and divide it by the area of each tile. The formula for the area of a rectangle is length times width. In this case, the base of the rectangle is given as m and the height is also given as m. Therefore, the area of the surface is m times m, which simplifies to m^2. Since the side length of each square tile is given as cm, we need to convert the area of the surface from m^2 to cm^2. Finally, we divide the converted area by the area of each tile, which is cm^2, to get the number of tiles needed.

Explanation
The area of a triangle is calculated by multiplying the base by the height and dividing by 2. In this case, since the triangle is isosceles, the base and height are equal. Therefore, we can take one side of the triangle as the base and the other side as the height. So, the area would be (x * x) / 2, where x is the length of one side. Since the sides of the triangle are given as "cm each," we can substitute x with the given length of the side, which is "cm." So, the area would be (cm * cm) / 2, which simplifies to cm^2 / 2. Since the sides are given as "cm each," the area would be cm^2 / 2. Therefore, the correct answer is 50 cm^2.

Explanation
The area of an equilateral triangle can be calculated using the formula A = (sqrt(3)/4) * s^2, where s is the length of the side of the triangle. In this case, the perimeter of the triangle is given as dm, which means that each side of the triangle is dm/3. The height of the triangle is given as cm. Using the Pythagorean theorem, we can calculate the length of the side of the triangle as sqrt((dm/3)^2 - cm^2). Plugging in the values and calculating, we find that the area of the triangle is 389.25 cm.

Explanation
The correct answer is 12 cm. The question states that the base of the parallelogram is "veces más" (times more) than its height. However, the number of times more is not specified. Therefore, we cannot determine the exact value of the base. However, since the only option that is larger than 9 cm (the given height) is 12 cm, it is the most reasonable choice for the base.

Explanation
The area of a rhombus can be calculated using the formula A = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals. In this question, it is given that the length of the larger diagonal is 30 cm and the length of the smaller diagonal is half of the larger diagonal. Therefore, the length of the smaller diagonal is 15 cm. Plugging these values into the formula, we get A = (30 * 15) / 2 = 450 / 2 = 225 / 2 = 112.5 cm². However, the answer options provided are all in whole numbers, so the closest option is 25 cm².