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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Here are the solutions for the questions: Question 1: Calculate the perimeter of the shape below? The shape is a composite figure consisting of a rectangle and a right-angled triangle. The top side of the rectangle is 16 cm. The slanted side of the triangle is 8 cm. The tick marks on the right vertical side of the rectangle and the base of the triangle indicate that these two lengths are equal. Let's call this common length x. So, the height of the rectangle is x, and the base of the triangle is x. Step 1: Identify the lengths of the sides for the perimeter. • Top horizontal side: 16 cm • Right vertical side: x cm • Bottom horizontal side: 16 cm (from the rectangle part) + x cm (from the triangle part) = (16 + x) cm • Left slanted side: 8 cm Step 2: Use the Pythagorean theorem to find x. The triangle is a right-angled triangle with legs x and x, and hypotenuse 8 cm. x^2 + x^2 = 8^2 2x^2 = 64 x^2 = (64)/(2) x^2 = 32 x = sqrt(32) x = sqrt(16 × 2) x = 4sqrt(2) cm Step 3: Calculate the perimeter by adding all the side lengths. Perimeter = 16 cm + x cm + (16 + x) cm + 8 cm Substitute x = 4sqrt(2) cm: Perimeter = 16 + 4sqrt(2) + (16 + 4sqrt(2)) + 8 Perimeter = 16 + 4sqrt(2) + 16 + 4sqrt(2) + 8 Perimeter = (16 + 16 + 8) + (4sqrt(2) + 4sqrt(2)) Perimeter = 40 + 8sqrt(2) cm The perimeter of the shape is 40 + 8sqrt(2) cm. Question 2: The shape below is called a? The shape shown is a three-dimensional object with two circular bases and a curved surface connecting them. The shape is called a cylinder. The shape is a cylinder. What's next? 3 done, 2 left today. You're making progress.