The high school debate team is developing a logo to represent their club. A scale drawing of the logo design is presented below, where each unit of the grid represents 3 inches in length. The team is printing out an enlargement of the new logo, where the enlargement has a height of 105 inches. The area of the enlargement will be inches2, which is times the size of the original scale drawing.

The enlargement will be 2,250 which is 25 the times

Step-by-step explanation:

In the provided scale drawing, each unit represents 3 inches in length. Use this scale to add the real world measurements to the scale drawing as shown.

It can be seen from the figure that the total height of the scale drawing is 9 in + 3 in + 9 in = 21 in. It is given that the enlargement has a height of 105 inches. Find the scale factor between the scale drawing and the enlargement by dividing as shown.

The scale factor of 5 means that each dimension of the enlargement will be 5 times larger than the matching dimension of the scale drawing. So, the dimensions of the enlarged figure are shown below.

The logo is made up of three polygons: two triangles and one square. To find the total area of the logo, the area of each region must be found and added together.

To calculate the area of a triangle, use the formula below where b is the length of the base of the triangle and h is the height of the triangle.

To calculate the area of a square, use the formula below, where s is the length of the side of the square.

Now, calculate the areas of of the two logos.

Finally, determine how many times larger the area of the enlargement is than the scale drawing by dividing, as shown below.

Therefore, the area of the enlargement will be 2,250 inches2, which is 25 times the size of the original scale drawing.