There are some number of two kinds of trapezoidal-shaped tile A and B shown as below respectively.
I will arrange A and B by connecting sides of A and B with 1cm in length and make figures such as Fig.1 and Fig.2.
For instance, as for Fig.1, it is a figure where three A tiles were arranged and Fig.2 is a figure where two A and two B were arranged.
Answer the following questions.
(1) I make a figure by arranging two A and six B.
Find the area ratio between the figure surrounded by inner sides of this figure and the figure surrounded by inner sides of Fig.2.
(2) I make a figure by arranging four A and two B.
Find the length of surroundings outside of the figure.
Answer
(1) 7：2
(2) 16 cm
Solution
(1) The figure is as shown in Fig.4 below.
Inside of this figure is rectangle and inside of Fig.2 is also rectangle.
The vertical length of both rectangles is same.
The horizontal length of the rectangle inside of Fig.4 is 2 + 3 + 2 = 7(cm).
The horizontal length of the rectangle inside of Fig.2 is 2cm.
Thus area ratio is also 7 : 2.
(2) The figure is as shown in Fig.5 below.
As you can see, the length of surroundings outside of the figure is 3 × 4 + 2 × 2 = 12 + 4 = 16 cm.
