Question

1. determine the area of the following shapes. round your answers to the nearest tenth of a square unit. a) image of rectangle with 6 cm (approx) and 2 cm b) image of triangle with base 8 cm and height 6 cm c) a circle with a diameter of 44 in.

Explanation:

Part (a)

Step1: Identify the shape and formula

The shape is a rectangle. The formula for the area of a rectangle is \( A = l \times w \), where \( l \) is the length and \( w \) is the width.
Here, \( l = 6 \, \text{cm} \) and \( w = 2 \, \text{cm} \).

Step2: Calculate the area

Substitute the values into the formula: \( A = 6 \times 2 \)
\( A = 12 \, \text{cm}^2 \)

Step1: Identify the shape and formula

The shape is a triangle. The formula for the area of a triangle is \( A=\frac{1}{2}\times b\times h \), where \( b \) is the base and \( h \) is the height.
Here, \( b = 8 \, \text{cm} \) and \( h = 6 \, \text{cm} \).

Step2: Calculate the area

Substitute the values into the formula: \( A=\frac{1}{2}\times8\times6 \)
First, calculate \( 8\times6 = 48 \), then \( \frac{1}{2}\times48 = 24 \)
So, \( A = 24 \, \text{cm}^2 \)

Step1: Find the radius

The diameter of the circle \( d = 44 \, \text{in} \). The radius \( r=\frac{d}{2} \), so \( r=\frac{44}{2}=22 \, \text{in} \).

Step2: Use the circle area formula

The formula for the area of a circle is \( A=\pi r^2 \). Substitute \( r = 22 \) into the formula: \( A=\pi\times(22)^2 \)
Calculate \( 22^2=484 \), so \( A = 484\pi \)
Using \( \pi\approx3.1416 \), \( A\approx484\times3.1416 \approx 1520.5 \, \text{in}^2 \) (rounded to the nearest tenth)

Answer:

\( 12 \, \text{cm}^2 \)

Part (b)