What is the answer?---1. The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches?
**Image Description:**
The image contains a grid of squares with a shaded region in the center. The grid is 6 squares wide and 5 squares tall. The question states the grid is made of 1-inch squares.
The shaded region is a geometric shape resembling a multiplication symbol or an 'X'. The shape is symmetrical.
The shaded area covers several full grid squares and several partial grid squares (triangles).
Specifically, the shaded area covers:
- 4 full squares in the central 2x2 area.
- 4 additional full squares, one immediately above, one below, one to the left, and one to the right of the central 2x2 area.
- 8 triangular areas, each occupying half of a grid square. These triangles are located at the corners of the central 2x2 area and at the outer edges of the shape.
The text "Math Team" is centered within the shaded area.
**Options:**
(A) 10
(B) 12
(C) 13
(D) 14
(E) 15
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Let's solve this step by step. We have a Math Team logo shaped like a multiplication symbol on a grid of one-inch squares. The logo consists of shaded squares and triangular regions. We need to find the total area of this logo.
Now let's count the full squares systematically. First, we have the central two by two area which contains four full squares. Then we have four extension squares: one above the center, one below, one to the left, and one to the right. That gives us a total of eight full squares, contributing eight square inches to the total area.
Now let's count the triangular areas. We have four corner triangles, each occupying half of a grid square, contributing two square inches total. We also have four edge triangles, each also half a square, adding another two square inches. The total area from all triangular regions is four square inches.
Now let's calculate the total area. We found 8 full squares contributing 8 square inches, and 8 triangular areas contributing 4 square inches. Adding these together: 8 plus 4 equals 12 square inches. Therefore, the area of the Math Team logo is 12 square inches, which corresponds to answer choice B.
To summarize what we've learned: When finding areas of complex shapes on grids, break them into simpler components. Count full squares and partial areas separately. Remember that triangular regions typically represent half a grid square. Our systematic approach gave us 8 full squares plus 4 square inches from triangular areas, totaling 12 square inches.