Question

SMCPS All About Area and Expressions Challenge 1: Drag the blue and red points so that the area of the red rectangle is 36 square units and the area of the blue rectangle is 45 square units. Find three different expressions for the total area. The first involves the two individual areas. The next two must ONLY use the values that are the dimensions of the two rectangles.

Description
Expression
Two areas
Uses dimensions of the two rectangles
Uses form (a/b+c) for distributive property

Answer 1

The total area of the red and blue rectangles is 81 square units. To use the dimensions for alternative expressions, the formula would involve the multiplication of the length and width for both rectangles with simplification. The area of the blue rectangle is 5/4 times the area of the red rectangle.

Step-by-step explanation:

To calculate the total area when given the areas of a red and a blue rectangle, we can start by using the sum of these individual areas. The area of the red rectangle is 36 square units, and the area of the blue rectangle is 45 square units. Therefore, the total area using the two individual areas is 36 + 45 = 81 square units.

For the other expressions that only use the dimensions of the rectangles, we assume the red rectangle has dimensions a x b and the blue rectangle has dimensions c x d. The blue area equals 45, so one dimension of the blue is 45/c or 45/d. A possible expression for the total area, using the distributive property, could then take the form (a x b) + (c x (45/c)) or (a x b) + ((45/d) x d), where we would distribute and simplify the expressions.

To compare the two areas using a ratio, we simply take the area of the larger square divided by the area of the smaller square: 45/36 = 5/4, or in words, the area of the blue rectangle is 5/4 times the area of the red rectangle.