Question

1. here are two similar shapes. the area of shape a is 60 cm². find the area of shape b. a b 10cm 20cm diagram not to scale 240cm² 120cm² 180cm² 200cm²

Explanation:

Step1: Find the scale factor of linear dimensions

The linear dimension of shape A is \( 10 \, \text{cm} \) and of shape B is \( 20 \, \text{cm} \). The scale factor \( k \) from A to B is \( \frac{20}{10} = 2 \).

Step2: Find the scale factor for areas

For similar shapes, the ratio of areas is the square of the ratio of corresponding linear dimensions. So the area scale factor is \( k^2 = 2^2 = 4 \).

Step3: Calculate the area of shape B

The area of shape A is \( 60 \, \text{cm}^2 \). Multiply by the area scale factor: \( 60 \times 4 = 240 \, \text{cm}^2 \).

Answer:

\( 240 \, \text{cm}^2 \) (corresponding to the option with \( 240 \, \text{cm}^2 \))