12. The shape shown is made up of three similar right-angled triangles.
The smallest triangle has two sides of side-length 2, as shown.
What is the area of the shape?

A 14
B $12+12 \sqrt{2}$
C 28
D $24+20 \sqrt{2}$
E 56
12. A Let the length of the hypotenuse of the smallest triangle be $l$. Then $l^{2}=2^{2}+2^{2}=8$. So $l=\sqrt{8}=2 \sqrt{2}$. Therefore the ratio of the lengths of the sides of the middle triangle to the lengths of the sides of the smallest triangle is $\sqrt{2}: 1$. Hence the corresponding ratio of the areas of these two triangles is $2: 1$. Similarly, the area of the largest triangle is twice the area of the middle triangle. Now the area of the smallest triangle is $\frac{1}{2} \times 2 \times 2=2$. Therefore, the area of the middle triangle is $2 \times 2=4$. Hence the area of the large triangle is $2 \times 4=8$. So the area of the shape is $2+4+8=14$.