Question

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

Explanation:

Step1: Calculate the area of the square

The area of a square \(A = s^2\), where \(s = 10\) cm. So \(A_1=10\times10 = 100\) cm².

Step2: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\). Here \(a = 10\) cm, \(b=6\) cm, \(h = 20-(10 + 3+5)=2\) cm. So \(A_2=\frac{(10 + 6)\times2}{2}=16\) cm².

Step3: Calculate the area of the rectangle

The area of a rectangle \(A = l\times w\). For the large - rectangle with \(l = 20\) cm and \(w = 6\) cm, \(A_3=20\times6=120\) cm². For the small - rectangle with \(l = 2\) cm and \(w = 4\) cm, \(A_4 = 2\times4=8\) cm².

Step4: Sum up the areas

\(A=A_1+A_2+A_3+A_4=100 + 16+120+30=266\) cm².

Answer:

266 cm²