Set 64
- 64 feet^2 .If one side of the square measures 8 feet, the other three
sides of the square each measure 8 feet. Multiply two sides of the
square to find the area: 8 feet ×8 feet = 64 square feet. - 100 feet^2. Sides and angles of a regular polygon are equal so, if
one side measures 10 feet, the other sides will also measure 10 feet.
The perimeter of this pentagon measures 50 feet (10 ×5 = 50) and
its apothem measures 4 feet, so the area of the pentagon measures
^12 ×4 feet ×50 feet = 100 square feet. - 9 3 feet^2 .To find the height of equilateral ΔDEF, draw a
perpendicular line segment from vertex E to the midpoint of DF.
This line segment divides ΔDEF into two congruent right
triangles. Plug the given measurement into the Pythagorean
theorem: (^12 ×6)^2 + b^2 = 6^2 ; 9 + b^2 = 36; b= 27 ; b= 3 3 .
To find the area, multiply the height by the base: 3 3 feet ×6 feet
= 18 3 square feet. Then, take half of 18 3 to get 9 3 . - 100 – r^2 + 1r
The area of the larger square will be 10 ×10 = 100. The area of the
smaller contained rectangle will be A= l×w= (r)(r– 1) = r^2 – 1r.
To find the area of the shaded region, subtract the smaller figure
from the larger: 100 – (r^2 – 1r) = 100 – r^2 + 1r. - 24 13 – 16 3
Solve for the height AO of ΔABC by using leg BO = 12,
hypotenuse AB = 14, and the Pythagorean theorem: 14^2 = 12^2 + a^2 ,
52 = a^2 , a= 2 13 . Then A= ^12 (b)(h) = ^12 (24)( 2 13 ) = 24 13 ,
which is the area of ΔABC. Do the same for ΔDEF using a leg of 4
and a hypotenuse of 8: 8^2 = b^2 + 4^2 , 48 = b^2 , 4 3 = b. Then A=
^12 (b)(h) = ^12 (8)(4 3 ) = 16 3 , which it the area of ΔDEF. Subtract
the area of ΔDEF from the area of ΔABC to get the shaded area.
501 Geometry Questions