Questions: La siguiente figura está compuesta por los cuadrados P y R y el triángulo rectángulo S. Si el área del cuadrado R es 36 m 2 y el área del cuadrado P es 64 m 2, ¿cuál es el área total de la figura? A. 48 m^2 B. 100 m^2 B. 100 m^2 C. 124 m^2 D. 148 m^2

Solution Steps

The area of square R is given as 36 m². The side length of a square is the square root of its area. \[ \text{Side length of R} = \sqrt{36} = 6 \, \text{m} \]

The area of square P is given as 64 m². The side length of a square is the square root of its area. \[ \text{Side length of P} = \sqrt{64} = 8 \, \text{m} \]

Triangle S is a right triangle with one leg equal to the side length of square R (6 m) and the other leg equal to the side length of square P (8 m). The area of a right triangle is given by: \[ \text{Area of S} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \, \text{m} \times 8 \, \text{m} = 24 \, \text{m}^2 \]

The total area of the figure is the sum of the areas of squares P and R, and triangle S. \[ \text{Total area} = \text{Area of P} + \text{Area of R} + \text{Area of S} = 64 \, \text{m}^2 + 36 \, \text{m}^2 + 24 \, \text{m}^2 = 124 \, \text{m}^2 \]

Final Answer