Question
The following figure is a rectangle made up of two smaller rectangles.
Top of the rectangle : 6
Side of the smaller rectangle: x
Side of the larger rectangle: 7
Bottom of the rectangle: 6
(a) Find the area of the following (in square units).
Thelightrectangle(onthe top):_
The dark rectangle(onthe bottom)_
(b) Give the area of the entire figure (in square units) in two different ways.
As a sum of two areas: _
As a product of the length and width: _
Top of the rectangle : 6
Side of the smaller rectangle: x
Side of the larger rectangle: 7
Bottom of the rectangle: 6
(a) Find the area of the following (in square units).
Thelightrectangle(onthe top):_
The dark rectangle(onthe bottom)_
(b) Give the area of the entire figure (in square units) in two different ways.
As a sum of two areas: _
As a product of the length and width: _
Answers
Answered by
GPT-4o mini
To solve the problem, we need to clarify what the figure looks like, which comprises a larger rectangle and a smaller rectangle positioned beneath it.
### Given Information:
- The width of the entire figure (rectangle) is \( 6 + 6 = 12 \) units (6 units on the top and 6 units on the bottom).
- The height of the larger rectangle is \( 7 \) units.
- The height of the smaller rectangle is defined as \( x \) units.
### (a) Finding areas
1. **Area of the light rectangle (on the top)**:
- The light rectangle's width is \( 12 \) units (same as the whole figure) and its height is \( 7 \) units (as specified).
- Area of the light rectangle = Width × Height = \( 12 \times 7 = 84 \) square units.
2. **Area of the dark rectangle (on the bottom)**:
- The width is again \( 12 \) units, and its height is \( x \) units.
- Area of the dark rectangle = Width × Height = \( 12 \times x \).
### (b) Area of the entire figure in two different ways
1. **As a sum of two areas**:
- Total area = Area of the light rectangle + Area of the dark rectangle.
- Total area = \( 84 + 12x \) square units.
2. **As a product of the length and width**:
- The total width of the whole figure is \( 12 \) units (as deduced before).
- The total height of the whole figure is \( 7 + x \) units (the height of the light rectangle plus the height of the dark rectangle).
- Total area = Length × Height = \( 12 \times (7 + x) \) square units.
### Summary of answers:
(a)
- Area of the light rectangle: **84** square units
- Area of the dark rectangle: **12x** square units
(b)
- Total area as a sum of two areas: **84 + 12x** square units
- Total area as a product of length and width: **12(7 + x)** square units
### Given Information:
- The width of the entire figure (rectangle) is \( 6 + 6 = 12 \) units (6 units on the top and 6 units on the bottom).
- The height of the larger rectangle is \( 7 \) units.
- The height of the smaller rectangle is defined as \( x \) units.
### (a) Finding areas
1. **Area of the light rectangle (on the top)**:
- The light rectangle's width is \( 12 \) units (same as the whole figure) and its height is \( 7 \) units (as specified).
- Area of the light rectangle = Width × Height = \( 12 \times 7 = 84 \) square units.
2. **Area of the dark rectangle (on the bottom)**:
- The width is again \( 12 \) units, and its height is \( x \) units.
- Area of the dark rectangle = Width × Height = \( 12 \times x \).
### (b) Area of the entire figure in two different ways
1. **As a sum of two areas**:
- Total area = Area of the light rectangle + Area of the dark rectangle.
- Total area = \( 84 + 12x \) square units.
2. **As a product of the length and width**:
- The total width of the whole figure is \( 12 \) units (as deduced before).
- The total height of the whole figure is \( 7 + x \) units (the height of the light rectangle plus the height of the dark rectangle).
- Total area = Length × Height = \( 12 \times (7 + x) \) square units.
### Summary of answers:
(a)
- Area of the light rectangle: **84** square units
- Area of the dark rectangle: **12x** square units
(b)
- Total area as a sum of two areas: **84 + 12x** square units
- Total area as a product of length and width: **12(7 + x)** square units