Question

what is the area of the composite figure? 262 cm² 264 cm² 266 cm² 268 cm²

Explanation:

1. First, analyze the composite - figure by splitting it into known geometric shapes (rectangles in this case).

• Top - left square: The side - length of the top - left square is \(s = 10\) cm, and its area \(A_1=10\times10 = 100\) \(cm^2\).
• Middle rectangle: The dimensions of the middle rectangle are \(l = 10\) cm and \(w = 4\) cm, so its area \(A_2 = 10\times4=40\) \(cm^2\).
• Bottom - left rectangle: The dimensions of the bottom - left rectangle are \(l = 20\) cm and \(w = 6\) cm, so its area \(A_3=20\times6 = 120\) \(cm^2\).
• Small rectangle on the right - side: The dimensions of the small rectangle on the right - side are \(l = 4\) cm and \(w = 2\) cm, so its area \(A_4=4\times2 = 8\) \(cm^2\).

1. Then, find the total area of the composite figure \(A\) by adding up the areas of these rectangles:

• \(A=A_1 + A_2+A_3+A_4\).
• \(A = 100+40 + 120+8\).
• \(A=268\) \(cm^2\).

Answer:

268 \(cm^2\)