# Moss's Egg. Task -1- Find the area of the shaded region inside the two circles shown below. The two large circles have a radius of 6cm.

Moss’s Egg

The following formulas were used in the solving of the questions of this assessment piece:

Working Out and Explanation

Task -1- Find the area of the shaded region inside the two circles shown below. The two large circles have a radius of 6cm. Their centres are A and B.

From the information given above, we know that the radii of the two larger circles are 6 cm in length. We define the radius of the circle as a straight line extending from the centre of a circle to its circumference. Since we know that points A and B are the centres of the two large circles, we can conclude that this is the length of the two points from A to B is 6 cm also, since point B is along the circumference of the top larger circle, and vice versa. From lengths A to B is the therefore the diameter of the smaller circle between the two larger ones, and thus we can conclude that the radius of the smaller circle is 3 cm. The area of the small circle can therefore be calculated using the formula indicated:                  , where A equals the area and r is the radius. Thus: A =  (32) = 9

28.3 cm2

Task -2- The same circles are shown below. Find the area and perimeter of the triangle ABC.

1. In order to determine the area of triangle ABC, we must adopt the formula: , where b is the base and h is the perpendicular height. From the information we are given, we know that the base of the triangle is 6 cm in length, as we know that this is the diameter of the small circle and that the base extends to its ends (A to B). What we don’t know however, is the triangle’s perpendicular height, and we must refer to the dynamics of the triangle to determine this. It is noticed that chords AC and BC both meet at the same location, the point which links the radius of the small circle (C) to its base (D). Therefore, triangle ABC is an isosceles triangle. Thus we see that point C extending directly below to the base triangle ABC is the radius of the small circle, which equals 3 cm. Therefore, to calculate the area, we simply substitute the information we have to the formula above:

Area of triangle ABC =  bh =   6  3

= 9 cm2

1. The properties of this triangle tell us that the perpendicular line of an isosceles triangle meets the base at angles of 900 and thus we have two right angles triangles. Therefore, we can find the lengths of the two sides using Pythagoras’ theorem. AC and BC are both considered as hypotenuses of their right angled triangles. We know that the perpendicular height of the triangle is 3 cm and AD and BD are 3 cm as well. Thus, AC2 = 33 + 32 = 18,     ...