Exam 9: Areas of Polygons and Circles

If two triangles have the same areas and the same length of altitude, these triangles must be congruent.

Find the exact area of a triangle whose sides measure 5, 6, and 7.

Find the area of a square whose apothem has length 7 cm.

and have the same length of base and the same length of altitude. If the area of is 25 , find the area of .

What expression represents the exact circumference of a circle with radius 6 inches?

For a given circle, the length of a 90° arc is one-third the circumference of the circle.

For a square with apothem of length a, the perimeter equals 4a.

Where P is the perimeter of a triangle whose inscribed circle has radius length r,the area of the triangle is A = rP.

In ,     . If MQ = 10, RP = 4, and MR = 8, find the area of .

The area of any regular polygon with length of apothem a and perimeter P is given by A = aP .

For a square whose length of apothem is a, find an expression containing a that represents the area A of the square.

In a circle of radius length 5, use an inequality of the form a x b to express possible lengths x for a chord.

For , radii and and arc bound a sector. If m = 100 ° and PX = 5.6 inches, find the area of the sector correct to the nearest tenth of a square inch.

For a circle of radius r , the area is given by A = 2 r .

The semiperimeter s of a triangle with sides of lengths a , b , and c is given by s = ( a + b + c ).

In ,     and in ,     . If AB = XY and CD = ZW , then:

For the segment bounded by chord and arc , CD = 12 cm and m = 120 ° .Find the exact area of the segment.