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.
ScanSolve AI Answer
a) Find the value of W Step 1: The shaded region is the top face of the rectangular prism. Its area is given as 56 cm^2. The dimensions of this face are length 8 cm and width W cm. The formula for the area of a rectangle is length × width. 8 cm × W cm = 56 cm^2 Step 2: Solve for W. 8W = 56 W = (56)/(8) W = 7 cm The value of W is 7 cm. b) Calculate its total surface area. Step 1: The dimensions of the rectangular prism are: Length (L) = 8 cm Width (W) = 7 cm (from part a) Height (H) = 5 cm The formula for the total surface area (TSA) of a rectangular prism is: TSA = 2(LW + LH + WH) Step 2: Substitute the values into the formula. TSA = 2((8 cm)(7 cm) + (8 cm)(5 cm) + (7 cm)(5 cm)) TSA = 2(56 cm^2 + 40 cm^2 + 35 cm^2) Step 3: Perform the addition and multiplication. TSA = 2(131 cm^2) TSA = 262 cm^2 The total surface area is 262 cm^2. Send me the next one 📸