Question

What fraction of a 2 x 2 square is shaded when forming an arrow by joining the bottom corners to the midpoint of the top edge and the center of the square?

a) 1/4
b) 1/2
c) 3/4
d) 1/3

Answer 1

The shaded portion of the 2 x 2 square when forming an arrow is 1/4 of the total area. One bottom triangle is half the size of the top triangle, making its area 1 square unit out of the total 4 square units.

Step-by-step explanation:

To determine what fraction of a 2 x 2 square is shaded when forming an arrow with the specifications given, first imagine the square (which has an area of 4 square units). By joining the bottom corners to the midpoint of the top edge, and the center of the square, you form two congruent triangles at the bottom and a larger triangle at the top. The area of the top triangle, which is now shaped like an arrow, is half the area of the square, or 2 square units.

Now, if you focus on just one of the bottom triangles, it is half the area of the top triangle, making it 1 square unit. Since the square has an area of 4 square units, the shaded bottom triangle is ¼ of the total area. Therefore, the answer is 1/4, which corresponds to option (a).

Applying this information to a related problem: Using the scale factor 1:4, and given that the scale dimension is 4, the actual dimension can be derived from the proportion 1:2 = 4:x. By cross-multiplication, you get x = 8 as the actual dimension.