Download Problem 1

Area Station Work
Problems #1-9 are meant to be “foundational” problems, where students can
review their understanding of the areas of triangles, trapezoids, parallelograms,
kites, regular polygons, and circles.
Problems #10-17 are meant to be “extension” problems, where students can really
extend their thinking and apply their understanding in a new way.
Problem 1:
The given circle has a radius of 6 and is inscribed in the square just touching at
points A, B, C, and D.
Find, to the nearest tenth, the area of the circle. Find the area of the square.
A
D
Problem 2:
Find the apothem of the regular
B
C
hexagon with side length of 12
and area of 374 units2.
12

a
Problem 3:
The sum of the lengths of the two bases of a trapezoid is 22 cm. The area of the
trapezoid is 66 cm2. What is the height of the trapezoid?
L (2, 12)
Problem 4:
Find the
(-4, 2) M
N (11, 2)
area of
LMN.
Problem 5: Find the area of ABCD.
Problem 6:
The perimeters of two squares are in a ratio of 4 to 9. What is the ratio between
the areas of the two squares?
Problem 7:
Problem 8:
Problem 9: Find the area of the shaded region.
Problem 10:
Find the area of the
the trapezoid.
(-6, 0)
(7, 4)
(-4, 4)
(3, 0)
shaded region of
(10, 0)
Problem 11:
If you have a hundred feet of rope to arrange into the perimeter of either a square
or a circle, which shape will give you the maximum area?
Ropes
Problem 12:
Find the shaded area to the nearest 0.1 cm2. The quadrilaterals shown are squares
and all arcs are arcs of a circle with radius 6 cm.
Problem 13:
Which is the biggest slice of pie: one-fourth of a 6-inch diameter pie, one-sixth of
an 8-inch diameter pie, or one-eighth of a 12-inch diameter pie?
Which slice has the most crust along its curved edge?
Justify how you know and include a picture to support your answer.
Problem 14:
A regular polygon has an area of 160 square units and a perimeter of 48 units.
Find the radius of the circle inscribed in the regular polygon.
Challenge:
Is there a way to determine the number of sides for this regular polygon? If so,
how do you do it? If you don’t think it’s possible to know, explain why.
Problem 15:
This diagram shows a circle with one square inside and one square outside.
a. What is the ratio of the areas of the two squares?
b. If a second circle is inscribed inside the smaller square, what is the ratio of
the areas of the two circles? Explain your reasoning.
Problem 16:
An acre is equal to 43,560 square feet. A 4-acre rectangular pasture has a 250-foot
side that is 40 feet from the nearest road. To the nearest foot, what is the distance
from the road to the far fence?
Start by drawing a diagram. Explain your reasoning.
Problem 17:
Dana buys a piece of carpet that measures 20 square yards. Will she be able to
completely cover a rectangular floor that measures 12 ft. 6 in. by 16 ft. 6 in.?
Explain why or why not.
Area Station Work
Problems #1-9 are meant to be “foundational” problems, where students can review their understanding of the
areas of triangles, trapezoids, parallelograms, kites, regular polygons, and circles.
Problems #10-17 are meant to be “extension” problems, where students can really extend their thinking and
apply their understanding in a new way.
Problem 1:
The given circle has a radius of 6 and is inscribed in the square just touching at points A, B, C, and D.
Find, to the nearest tenth, the area of the circle. Find the area of the square.
A
D
B
C
Problem 2:
Find the apothem of the regular hexagon with side length of 12 and area of 374 units2.
12

a
Problem 3:
The sum of the lengths of the two bases of a trapezoid is 22 cm. The area of the trapezoid is 66 cm2. What is
the height of the trapezoid?
Problem 4: Find the area of
LMN.
L (2, 12)
(-4, 2) M
N (11, 2)
Problem 5: Find the area of ABCD.
Problem 6:
The perimeters of two squares are in a ratio of 4 to 9. What is the ratio between the areas of the two squares?
Problem 7:
Problem 8:
Problem 9: Find the area of the shaded region.
Problem 10:
Find the area
(7, 4)
(-4, 4)
(-6, 0)
(3, 0)
of the shaded region of the trapezoid.
(10, 0)
Problem 11:
If you have a hundred feet of rope to arrange into the perimeter of either a square or a circle, which shape will
give you the maximum area?
Ropes
Problem 12:
Find the shaded area to the nearest 0.1 cm2. The quadrilaterals shown are squares and all arcs are arcs of a
circle with radius 6 cm.
Problem 13:
Which is the biggest slice of pie: one-fourth of a 6-inch diameter pie, one-sixth of an 8-inch diameter pie, or
one-eighth of a 12-inch diameter pie?
Which slice has the most crust along its curved edge?
Justify how you know and include a picture to support your answer.
Problem 14:
A regular polygon has an area of 160 square units and a perimeter of 48 units. Find the radius of the circle
inscribed in the regular polygon.
Challenge:
Is there a way to determine the number of sides for this regular polygon? If so, how do you do it? If you
don’t think it’s possible to know, explain why.
Problem 15:
This diagram shows a circle with one square inside and one square outside.
a.
b.
What is the ratio of the areas of the two squares?
If a second circle is inscribed inside the smaller square, what is the ratio of the areas of the two circles?
Explain your reasoning.
Problem 16:
An acre is equal to 43,560 square feet. A 4-acre rectangular pasture has a 250-foot side that is 40 feet from the
nearest road. To the nearest foot, what is the distance from the road to the far fence?
Start by drawing a diagram. Explain your reasoning.
Problem 17:
Dana buys a piece of carpet that measures 20 square yards. Will she be able to completely cover a rectangular
floor that measures 12 ft. 6 in. by 16 ft. 6 in.? Explain why or why not.