This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Problem 1: The first shape is a triangle with a given base and height. Step 1: Identify the formula for the area of a triangle. The area of a triangle (A) is calculated using the formula: A = (1)/(2) × base × height Step 2: Substitute the given values into the formula. From the image, the base (b) is 5 cm and the height (h) is 17 cm. A = (1)/(2) × 5 cm × 17 cm Step 3: Calculate the area. A = (1)/(2) × 85 cm^2 A = 42.5 cm^2 The area of the triangle is 42.5 cm^2. Problem 2: The second shape consists of two concentric circles, and we need to find the area of the region between them (an annulus). We are given the diameters and instructed to use = (22)/(7). Step 1: Determine the radii of the outer and inner circles. The radius is half of the diameter. Outer radius (R) = 56 cm2 = 28 cm Inner radius (r) = 5 cm2 = 2.5 cm Step 2: Identify the formula for the area of an annulus. The area of an annulus (A) is the difference between the area of the outer circle and the area of the inner circle: A = R^2 - r^2 = (R^2 - r^2) Step 3: Substitute the values into the formula. A = (22)/(7) ((28 cm)^2 - (2.5 cm)^2) Step 4: Calculate the squares of the radii. R^2 = (28)^2 = 784 cm^2 r^2 = (2.5)^2 = 6.25 cm^2 Step 5: Substitute the squared values and calculate the difference. A = (22)/(7) (784 cm^2 - 6.25 cm^2) A = (22)/(7) (777.75 cm^2) Step 6: Perform the final multiplication and division. A = (22 × 777.75)/(7) cm^2 A = (17110.5)/(7) cm^2 A ≈ 2444.36 cm^2 The area of the shape is 2444.36 cm^2. Send me the next one 📸