Question

A trapezoid has base lengths of 12 centimeters and 13 centimeters. The other sides have lengths of 5 centimeters and 10 centimeters. A rectangle with side lengths of 2 centimeters and 5 centimeters is connected to the side with length 10 centimeters.
What is the area of the composite figure?

Answer 1

Answer:

The area of the composite figure is 392.12$cm^{2}$.

Step-by-step explanation:

The area of the composite figure = area of trapezoid + area of rectangle

Area of trapezium = $\frac{1}{2}$ ( a +b)h

Where: a is the length of the first base, b the length of the second base and h is the height of the trapzium.

Applying Pythagoras theorem, the height, h, is;

h = $\sqrt{5^{2} - 1^{2} }$

  = $\sqrt{24}$

h  = 2$\sqrt{6}$

Area of trapezium = $\frac{1}{2}$ ( a +b)h

                              = $\frac{1}{2}$ (13 + 12) × 2$\sqrt{6}$

                              = 156$\sqrt{6}$

                              = 382.12$cm^{2}$

Area of trapezium is 382.12$cm^{2}$

Area of rectangle = length × width

                             = 5 × 2

                             = 10 $cm^{2}$

Area of rectangle = 10 $cm^{2}$

Therefore,

area of the composite figure = 382.12 + 10

                                               = 392.12$cm^{2}$