Geometry
Name: _____________________________
#4 Finding Unknowns Dimensions & Shaded Area
Period: ____
Show all work – Record formula, substitute in given info use π and record exact answers in terms of π - no
decimals please. Also simplify fractions to lowest terms.
1. If the base of a triangle is 12 cm and the area is 42
cm find the height and then find the area.
2. If the base of a rectangle is 8 cm and the perimeter
is 60 cm find the find the height and then find the
area.
3. If the area of a circle is 81π cm2. Find the
circumference.
4. If the circumference of a circle is 15π inches. Find
the area.
5. If the area of a circle is 32π cm2. Find the
circumference.
6. If the circumference of a circle is 20 inches. Find
the area.
7. A right triangle with area 90 cm2 and one leg 12
cm. Find the perimeter.
8. A right triangle with area 50 3 cm2 and one leg 10
cm. Find the perimeter.
A = 90cm2
A = 50 3 cm2
12 cm
9. What is the area of a circle whose circumference
is π.
10 cm
10. Circle and a rectangle (with base 24 cm and height
10 cm). Find shaded area.
8
24
11. Two circles. The circumference of the large circle is
24π cm. Find the shaded area.
13. Find the perimeter and the shaded area.
12. One larger semicircle with diameter 16 cm and two
smaller semicircles. Find the perimeter and the
shaded area.
14. Find the shaded area.
6 cm
8 cm
12
15. The cross has all 12 sides congruent and equal to 5.
All angles are right angles. Find the shaded area.
16. Semicircle with isosceles triangle. Which of the
following is the exact perimeter of the figure?
D = 8 cm
12 cm
17. Three semicircles are drawn from the midpoints of
the three sides of the triangle. Find the area of the
triangle and the area of the shaded region.
10
24
18. The circle below has an area of 25and is divided
into 8 congruent regions. What is the perimeter of
one of these regions?
19. In the figure below, a small square is inside a larger
square. What is the area, in terms of x, of the
shaded region?
x
5
x
5
20. In the figure below, the smaller circles each have a
radius of 3. What is the perimeter of the shaded
region?
21. The figure below consists of two circles that have
the same center. If the shaded area is 64square
inches and the smaller circle has a radius of 6
inches, what is the radius, in inches, of the larger
circle?
Note: Figure not to scale.
22. In rectangle PQRS below, arcs QT and RT are
quarter circles with centers at P and S, respectively.
If the radius of each quarter circle is 1, what is the
area of the shade region?
23. The circumference of the circle shown below is 2.
What is the area of the shaded region?