This design was formed by cutting 4 equal sectors from a circle that had an area 50 cm2.The remaining coloured sectors each have an angle at the centre of 80°. Work out the the total area of the coloured design, to the nearest square centimetre.Area of the design =  cm2 (to nearest sq cm)

To solve this problem, we need to understand that the area of a circle is proportional to the angle that a sector makes at the center of the circle.

Step 1: Calculate the total angle of the colored sectors. Since each colored sector has an angle of 80° at the center, and there are 4 colored sectors, the total angle for the colored sectors is 80° * 4 = 320°.

Step 2: Calculate the proportion of the circle that the colored sectors represent. A full circle is 360°, so the colored sectors represent 320° / 360° = 0.888... of the circle.

Step 3: Calculate the area of the colored sectors. Since the colored sectors represent 0.888... of the circle, and the total area of the circle is 50 cm², the area of the colored sectors is 0.888... * 50 cm² = 44.44 cm².

Step 4: Round to the nearest square centimeter. The area of the colored sectors is approximately 44 cm² when rounded to the nearest square centimeter.

So, the total area of the colored design is 44 cm².