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The perimeter of a regular polygon is 48 cm and its apothem is 6 cm. What is the area of the polygon?


A garden plot is to contain 128 sq. ft. If its length is to be twice its width, what should its dimensions be?



A certain city block is in the form of a parallelogram. Two of its sides are each 42 m. long; the other two sides are each 22 m. in length. If the distance between the first pair of sides is 12 m., find the area of the land in the block, and the length of the diagonals.



A square is a quadrilateral that has parallel opposite sides, perpendicular consecutive sides, and perpendicular diagonals. Determine and explain is the shown quadrilateral a square.


A toy train set has a circular track peace the inner radius of the piece is 6 cm one sector of the truck has an arc length of 33 cm on the inside and 55 cm on the outside. What is the width of the track?


The famous Eratosthenes experiment, that can be found at https://www.famousscientists.org/eratosthenes/, relied on the fact known to Thales and others that a beam of parallels cut by a transverse straight line determines equal measure for the corresponding angles. Given two similar triangles, one with small measurements that can be accurately determined, and the other with large measurements, but at least one is known with accuracy, can the other two measurements be deduced? Explain and give an example.
The similarity of triangles gives rise to trigonometry.
How could we understand that the right triangles of trigonometry with a hypotenuse of measure 1 represent all possible right triangles?

1.The sum of the perimeters of two squares is 50 cm and the sum of the areas is 93.25 cm^2. Find the side length of each square.


2. The sum of the circumferences of two circles is 36π cm and the sum of the areas is 170π cm^2. Find the radius of each circle.


3. A cuboid has sides of length 5 cm, x cm and y cm. Given x+y=20.5 and the volume of the cuboid is 360 cm^3, find the value of x and the value of y.


1.The sum of the perimeters of two squares is 50 cm and the sum of the areas is 93.25 cm^2. Find the side length of each square.

2. The sum of the circumferences of two circles is 36π cm and the sum of the areas is 170π cm^2. Find the radius of each circle.

3. A cuboid has sides of length 5 cm, x cm and y cm. Given x+y=20.5 and the volume of the cuboid is 360 cm^3, find the value of x and the value of y.
The diagram shows a solid formed by joining a hemisphere, of radius r cm, to a cylinder, of a radius r cm and height h cm.

The total height of the solid is 18 cm and the surface area is 205π cm^2.

Find the value of r and the value of h.
1.The sum of the perimeters of two squares is 50 cm and the sum of the areas is 93.25 cm^2. Find the side length of each square.

2. The sum of the circumferences of two circles is 36π cm and the sum of the areas is 170π cm^2. Find the radius of each circle.

3. A cuboid has sides of length 5 cm, x cm and y cm. Given x+y=20.5 and the volume of the cuboid is 360 cm^3, find the value of x and the value of y.
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