find the area of shaded part(1 square=1cm2
Answers
Answer:
Triangle 1: the height is 1 and the base is 4 (or you can look at it the opposite way, doesn’t matter) so the area of that triangle is 2 cm^2.
Triangle 2: the height is 2 and the base is 3 so the area of that triangle is 3 cm^2.
Triangle 3: the height is 2 and the base is 2 so the area of that triangle is 2 cm^2.
Triangle 4: the height is 2 and the base is 6 so the area of that triangle is 6 cm^2.
Now that all of the areas have been calculated, we simply subtract them from the area of the rectangle: 24 - (2 + 3 + 2 + 6) = 24 - 13 = 11 cm^2
ABCD is a square of 2 cm. There are five equal circle of center A, B, C, D and O. What is the area of the shaded region?
This is where a diagram would be worth a thousand words.
I will assume the 5th circle (with center O) is centered at the center of the 2 cm square and that the 4 corner circles all touch the center circle. Since the circles have equal radii, the radius is 1/4 the diagonal of the square.
Radius = r = diagonal/4 = (2^2+2^2)^(1/2)/4 = (4+4)^(1/2)/4 = 8^(1/2)/4
r = 2*2^(1/2)/4 = 2^(1/2)/2
r^2 = 2/4 = 1/2
Shaded area = area of square less area of circles inside the square.
Shaded area = 2*2, less center circle, less 1/4 of the 4 corner circles
Shaded area = 4 - PI()*r^2 - (1/4)*4*PI()*r^2
Shaded area = 4 - 2*PI()*r^2
Shaded area = 4 - 2*PI()*(1/2) = 4 - PI() = 0.8584 cm^2