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

Answer

Explanation:

Step1: Divide the figure into rectangles and a trapezoid

We can divide the composite - figure into three rectangles and one trapezoid.

Step2: Calculate the area of the top - rectangle

The top - rectangle has length (l = 10) cm and width (w = 10) cm. The area of a rectangle is (A_{1}=l\times w), so (A_{1}=10\times10 = 100) (cm^{2}).

Step3: Calculate the area of the middle - left rectangle

The middle - left rectangle has length (l = 3) cm and width (w = 4) cm. So (A_{2}=3\times4=12) (cm^{2}).

Step4: Calculate the area of the middle - right rectangle

The middle - right rectangle has length (l = 5) cm and width (w = 4) cm. So (A_{3}=5\times4 = 20) (cm^{2}).

Step5: Calculate the area of the bottom rectangle

The bottom rectangle has length (l = 20) cm and width (w = 6) cm. So (A_{4}=20\times6=120) (cm^{2}).

Step6: Calculate the area of the trapezoid

The trapezoid has bases (b_{1}=4 + 3+5=12) cm and (b_{2}=20) cm, and height (h = 2) cm. The area of a trapezoid is (A=\frac{(b_{1}+b_{2})h}{2}), so (A_{5}=\frac{(12 + 20)\times2}{2}=32) (cm^{2}).

Step7: Calculate the total area

The total area of the composite figure (A = A_{1}+A_{2}+A_{3}+A_{4}+A_{5}). (A=100 + 12+20+120+32=264) (cm^{2}).

Answer:

264 (cm^{2})