Problem of the Week Chapter 11.1-11.3 (LTF)
Name ______________________________
Each problem is worth 3 points, 1 point for the answer 2 points for the work.
Period ______
1) In a given isosceles triangle the base angles are 30 . If the leg length is 20 cm, then what is the
area of the triangle?
A. 115.470 cm 2
B. 173.205 cm 2
C. 200 cm 2
D. 346.410 cm2
E. 400 cm 2
2) An equilateral triangle has sides of length x and a square has sides of length y. The sum of the
perimeters of the equilateral triangle and the square is 24 inches. What value of x will result in the
smallest sum of the areas of the triangle and the square?
A. 2.043
B. 3.429
C. 4.520
D. 10.090
E. 15.659
3) An isosceles triangle is inscribed in a semicircle with a radius of 6 cm. What is the area of the
region in square centimeters, that is outside the triangle but inside the semi-circle?
A. 20.549
B. 38.549
C. 56.549
D. 77.097
E. 113.097
4) If one of the diagonals of a rhombus is 12 in., and the length of a side is 10 in., then what is the
height, h, of the rhombus?
h
A. 8
B. 9.6
C. 13.856
D. 16
E. 19.496
5) The graph below shows the shaded region bounded by the y-axis, the x-axis, the line x  9 and the
graph f  x   1  x . Calculate the approximate area of the region by using the sum of the areas of
three trapezoids, one on the interval from x  0 to x  1 , the second on the interval from x  1 to
x  4 and the third on the interval from x  4 to x  9 .
A. 22.0
B. 22.5
C. 24.0
D. 26.5
E. 27.5
6) The triangle drawn below is a 30-60-90 triangle. What is the equation for the area, A , of
the triangle in terms of its hypotenuse, c ?
B
c
R
C
c2 3
A. A 
8
c2 3
B. A 
4
c2 3
C. A 
6
c2 2
D. A 
6
c2 2
E. A 
8
7) The lines listed below form the boundaries of a region. What is the area, in square units,
of the region?
2

y  3 x  2

x  0
x  3

 y  2
A. 6
B. 9
C. 12
D. 14
E. 15