1) prove that the circumcenter of an equilateral triangle is the same as its centroid i) calculate the length of the side of an
equilateral triangle with vertices on a circle of diameter 1cm ii) calculate the perimeter of such a triangle please, guys, help with this please with an easy answer thanking you in advance
1 answer:
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ANSWER:
1) 25.70 cm 2) 30.84 cm 3) 10.71 km 4) 1.07 km 5) 6.71 cm 6) 10.07 mm
EXPLANATION:
<em>1. Know that the circumference formula for a full circle is:</em>
The value of pi () = 3.14
The radius () will be given in the diagrams.
<em>2. Now we can figure out the perimeters. </em>
<u>Shape One: Semi-circle</u>
C = 2 x 3.14 x 5
C = 31.4 cm
Divide the circumference by 2 because it is a semi-circle. Then add 10 cm to this (because the flat side is 10 cm).
P =
P = 25.7 cm ≈ 25.70 cm
<u>Shape Two: Semi-circle</u>
C = 2 x 3.14 x 6 (the picture shows the diameter so we need to half that to get the radius)
C = 37.68 cm
Divide the circumference by 2 because it is a semi-circle. Then add 12 cm to this (because the flat side is 12 cm).
P =
P = 30.84 cm
<u>Shape Three: Quadrant</u>
C = 2 x 3.14 x 3
C = 18.84 km
Divide the circumference by 4 because it is a quadrant. Then add 6 km to this (because the two flat sides are 3 km each and so it is 6 km total).
P =
P = 10.71 km
<u>Shape Four: Quadrant</u>
C = 2 x 3.14 x 0.3
C = 1.884 km
Divide the circumference by 4 because it is a quadrant. Then add 0.6 to this (because the two flat sides are 0.3 km each and so it is 0.6 km total).
P =
P = 1.071 km ≈ 1.07 km
<u>Shape Five</u>
C = 2 x 3.14 x 1
C = 6.28 cm
For this shape, we need to subtract the circumference of the missing sector from the circumference of the full circle to obtain the circumference for this shape. So, the circumference for the shape would be:
C =
C = 6.28 - 1.57
C = 4.71 cm
Then add the flat sides (1 cm + 1 cm = 2 cm) to this circumference to get the perimeter.
P = 4.71 + 2
P = 6.71 cm
<u>Shape Six</u>
C = 2 x 3.14 x 1.5 (Divide the 3 mm diameter by 2 to get the radius)
C = 9.42 cm
Do the same thing you did for Shape 5.
C =
C = 7.065 mm
Then add the flat sides (1.5 + 1.5 = 3) to this circumference.
P = 7.065 + 3
P = 10.065 mm ≈ 10.07 mm