Question

what is the area of the composite figure?
262 cm²
264 cm²
266 cm²
268 cm²
(the figure has dimensions: top square 10 cm x 10 cm, lower parts with various lengths like 3 cm, 5 cm, 4 cm, 2 cm, 4 cm, 6 cm, 8 cm, 20 cm)

Explanation:

Step1: Calculate the area of the square

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

Step2: Calculate the area of the rectangle at the bottom

The area of a rectangle is \(A = l\times w\), where \(l = 20\) cm and \(w = 6\) cm. So \(A_2=20\times6=120\) \(cm^2\).

Step3: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\). Here, \(a=(20-(3 + 5))=12\) cm, \(b = 10\) cm, \(h=(4)\) cm. So \(A_3=\frac{(12 + 10)\times4}{2}=\frac{22\times4}{2}=44\) \(cm^2\).

Step4: Calculate the total area

\(A=A_1+A_2+A_3\). Substitute \(A_1 = 100\), \(A_2=120\), \(A_3 = 44\) into the formula. \(A=100+120 + 44=264\) \(cm^2\).

Answer:

\(264\ cm^2\)