Question

Each square and figure DNE has a side length of one unit compare the area of the two figures which figure has more area how much more explain or show your reasoning

Answer 1

Answer:

✅Figure E has more area

✅Figure E has 5.14 units² much more than Figure D.

Step-by-step explanation:

The logic to solving this kind of problem is to decompose and each of the figure to find out how many squares and circles are there in each figure, them calculate the area of each figure using the formula for area of square and area of a circle.

✍️Figure D:

Figure D is composed of 2 squares and 4 semicircles (2 full circles).

Since side length of 1 square = 1 unit, therefore, radius of the semi-circle/circle = 1 unit.

Area of the 2 squares = 2(s²) = 2(1²) = 2 unit²

Area of the 2 full circles = 2(πr²) = 2(3.14*1²) = 6.28 unit²

Area of Figure D = 2 + 6.28 = 8.28 unit²

✍️Figure E:

Figure E is composed of 4 squares and 6 quarter circles (3 full circles).

Area of the 4 squares = 4(s²) = 4(1²) = 4 unit²

Area of the 3 full circles = 3(πr²) = 3(3.14*1²) = 9.42 units²

Area of figure E = 4 + 9.42 = 13.42 unit²

✅Therefore, we can conclude that Figure E has more area.

✅Figure E has 5.14 unit² more area than Figure D (13.42 - 8.28 = 5.14).