Question

section b

1. what algebraic expression represents the area of the shaded region represented on the right?

the algebraic expression that represents the area of the shaded region is ______ .

1. consider the sequence of the following figures made of equilateral triangles with a side of 1 unit.

figure 1\tfigure 2\tfigure 3\t…
\t\t\t
\t\t\t
\t\t\t…
a) how many equilateral triangles has the nth figure?
the nth figure has ______ .
b) what is the perimeter of the nth figure?
the perimeter of the nth figure is ______ .

1. a pyramid with a square base and a cube have the same total area. the side of the base of the pyramid is 40 cm and its slant height is 10 cm. what is the measure of the edge of the cube?

the edge of the cube measures ______ .

1. in archery, eric has 60% chance of reaching the target. he throws a dart twice at the target. what is the probability that he reaches the target at least once?

the probability eric reaches the target at least once is ______ .

Explanation:

Question 7

Step1: Find area of outer rectangle

The outer rectangle has length \(4x + 3\) and width \(6\), so area is \(6(4x + 3)=24x + 18\).

Step2: Find area of inner rectangle

The inner rectangle has length \(3x - 2\) and width \(4\), so area is \(4(3x - 2)=12x - 8\).

Step3: Subtract inner area from outer area

Shaded area = Outer area - Inner area = \((24x + 18)-(12x - 8)=24x + 18 - 12x + 8 = 12x + 26\).

Step1: Analyze Figure 1,2,3

• Figure 1: \(1 = 1^2\) triangles.
• Figure 2: \(4 = 2^2\) triangles.
• Figure 3: \(9 = 3^2\) triangles.

Step2: Generalize for nth figure

The pattern shows the nth figure has \(n^2\) equilateral triangles.

Step1: Analyze perimeters

• Figure 1: Side length 1, perimeter \(3\times1 = 3\).
• Figure 2: Perimeter \(3\times2 = 6\).
• Figure 3: Perimeter \(3\times3 = 9\).

Step2: Generalize for nth figure

The pattern shows the perimeter of the nth figure is \(3n\).

Answer:

\(12x + 26\)

Question 8a