Question

find the perimeter or circumference and area of each figure. round answers to the nearest tenth, if necessary.

1. a(0, 9) y b(4, 9)

c(0, 1)
o x
area _____________
perimeter _____________

1. y

a(2, 3)
b(4, 1)
o x
area _____________
perimeter _____________
c = 2 π r
c = 2 π (√(4-2)² + (1-3)²)
c = 2 π (√(4 + 4))
c = 2 π (√8)
c = 2 π (2√2)
c = 4√2 π

Explanation:

Problem 4: Triangle \(ABC\) with \(A(0,9)\), \(B(4,9)\), \(C(0,1)\)

Area Calculation:

Step 1: Identify base and height

The base \(AB\) is horizontal. Length of \(AB\): \(|4 - 0| = 4\). The height is vertical distance from \(C\) to \(AB\): \(|9 - 1| = 8\).

Step 2: Use triangle area formula \(A = \frac{1}{2} \times \text{base} \times \text{height}\)

\(A = \frac{1}{2} \times 4 \times 8\)

Step 3: Calculate

\(A = 16\)

Perimeter Calculation:

Step 1: Find lengths of \(AC\), \(AB\), and \(BC\)

• \(AC\): Vertical distance, \(|9 - 1| = 8\)
• \(AB\): Horizontal distance, \(|4 - 0| = 4\)
• \(BC\): Use distance formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). For \(B(4,9)\) and \(C(0,1)\): \(d = \sqrt{(4 - 0)^2 + (9 - 1)^2} = \sqrt{16 + 64} = \sqrt{80} \approx 8.94\)

Step 2: Sum the sides

Perimeter \(= 8 + 4 + 8.94 \approx 20.94\), rounded to nearest tenth: \(20.9\)

Answer:

(Problem 4):
Area: \(16\)
Perimeter: \(\approx 20.9\)

Problem 5: Circle with center \(A(2,3)\) and point \(B(4,1)\) (radius is distance \(AB\))

Radius Calculation:

Step 1: Use distance formula for \(A(2,3)\) and \(B(4,1)\)

\(r = \sqrt{(4 - 2)^2 + (1 - 3)^2} = \sqrt{4 + 4} = \sqrt{8} \approx 2.828\)

Area Calculation:

Step 1: Use circle area formula \(A = \pi r^2\)

\(A = \pi (\sqrt{8})^2 = 8\pi \approx 25.1\) (rounded to nearest tenth)

Circumference (Perimeter) Calculation:

Step 1: Use circle circumference formula \(C = 2\pi r\)

\(C = 2\pi \sqrt{8} \approx 2 \times 3.1416 \times 2.828 \approx 17.8\) (rounded to nearest tenth)