Final Answer:
The area of the rectangle is 8.0cm ²
Step-by-step explanation:
o find the area of the rectangle, we start by considering that the two circles within the rectangle each touch three sides of the rectangle and each other. The diameter of each circle is equal to the width of the rectangle (2.0 cm). Therefore, the radius of each circle is r= 2.0 / 2 =1.0cm. The area of one circle is πr ² =π×1.0 ² =πcm ². As there are two circles, their combined area is 2×πcm².
The total area of the rectangle is the sum of the area of the two circles and the remaining area of the rectangle not occupied by the circles. The area of the rectangle is calculated as length multiplied by width, which is
4.0cm×2.0cm=8cm ² . To find the area not occupied by the circles, we subtract the combined area of the circles from the total area of the rectangle: 8cm ² −2×πcm ² =8cm ²−2πcm ² ,
Thus The area of the rectangle is 8.0cm ²