Honors Geometry Chapter 9 Test
A of circle = π(5)² = 25πcm² A of square = 30² = 900 cm² figure = square - circle = 900-25π ≈ 821.46 cm²
a figure is shaped like a square with a circle cut from the center of it. how many square centimeters is the area of the figure? round to the nearest hundredth.
geometric probability
a form of theoretical probability determined by a ratio of geometric measures such as lengths, areas, or volumes
composite figure
a plane figure made up of triangles, rectangles, trapezoids, circles, and other simple shapes, or a three-dimensional figure made up of prisms, cones, pyramids, cylinders, and other simple three-dimensional figures
P = 36 36 = 4s s = 9 cm A = s² 9² = 81 cm² A tripled = 81 x 3 = 243 cm² since the height remains constant, if it's area is tripled, the base length is also tripled
a square has a perimeter of 36 cm. if the area of a square is tripled and its height remains constant. what happens to its base length?
d = 10ft r = 5ft A = πr² A = 3.14(5)² A = 78.5 ft² d = 18ft r = 9ft A = πr² A = 3.14(9)² A = 254.3 ft² d = 26ft r = 13ft A = πr² A = 3.14(13)² A = 530.7 ft²
a store sells circular rugs in three different sizes. the rugs come in diameters of 10ft, 18ft, and 26ft. find the areas of the three different sizes of rugs. use 3.14 for π and round answers to the nearest tenth.
central angle of a regular polygon
an angle whose vertex is the center of the regular polygon and whose sides pass through consecutive vertices
A = πr²
area of a circle
A = ½d₁d₂
area of a kite
A = bh
area of a parallelogram
A = bh
area of a rectangle
A = ½(aP)
area of a regular n-gon
A = ½d₁d₂
area of a rhombus
A = s²
area of a square
A = (b₁ + b₂)h / 2
area of a trapezoid
A = ½bh
area of a triangle
C = πd or C = 2πr
circumference of a circle
A of ↑ ∆ = ½(5)(13) = 32.5 A of ↓ ∆ = ½(5)(13) - 1 = 31.5 the areas are not the same because the bottom triangle is missing one square so it's area is one unit less than the top triangle.
compare the areas of the two figures and explain why they are or are not the same.
d = √(x₂-x₁)² + (y₂-y₁)²
distance formula
*count whole and half squares* A ≈ 50.5 m²
estimate the area of the irregular shape. the grid has squares with side lengths of 1 m
A of parallelogram = 2[½(10)(5)] = 50in² A of parallelogram = A of rect. wtih height h and width 6 50 = 6h h = 8.333333333in
find h in the parallelogram
*graph the polygon* AD and BC are vertical lines AB and DC are horizontal lines vertical and horizontal lines are ⊥ so all 4 ∠s are right ∠s, and ABCD is a rectangle l = 4 (units between B and C/A and D w = 10 (units between A and B/D and C A = lw A = 10(4) = 40 units² P = 2(4) + 2(10) = 28 units
find the area and perimeter of a polygon with vertices A(-2, 5), B(8, 5), C(8, 1), and D(-2, 1).
*graph triangle and draw imaginary rectanlge around it with the vertices touching the sides* A of rect. = 7(6) = 42 units² A of small left ∆ = ½(7)(1) = 3.5 units² A of small upper right ∆ = ½(5)(5) = 12.5 units² A of small lower right ∆ = ½(2)(6) = 6 units² A of big ∆ = 42 - 3.5 - 12.5 - 6 = 20 units²
find the area of a triangle with vertices A(3, 8), B(8, 3), and C(2, 1).
d = 36 r = 36/2 = 18 A = πr² A = π18² A=324πft²
find the area of the circle in terms of π
A of rect. = 9(5) = 45 in² A of 2 ∆s = 2[½(6.5)(5) = 32.5 in² A of whole figure = 45 + 32.5 = 77.5 in²
find the area of the composite figure
A = bh 10² = 6² + h² 100 = 36 + h² 64 = h² 8 = h A = 15(8) = 120in²
find the area of the parallelogram
A = ½aP P = 10(6) = 60cm s = 5 hyp. = 2(5) = 10 a(pothem) = 5√3 A = ½(5√3)(60) A = 150√3 A ≈ 259.8 cm²
find the area of the regular hexagon with side lengths of 10 meters
A = ½d₁d₂ = ½(14x-6)(8x+7) A = ½(112x² + 98x - 48x -42) A = ½(112x² + 50x - 42) A = 56x² + 25x = 21
find the area of the rhombus
A of rect. = 8.5 x 14 = 119 ft² A of ½circle = πr²/2 = π7²/2 ≈77.0 ft² A of shaded = rect - ½circle A = 119 - 77 = 42.0 ft²
find the area of the shaded region. round to the nearest tenth.
A = ½ (b₁+b₂)(h) A = ½ (10+24)(7) = 119
find the area of the trapezoid
new car = 120° whole circle = 360° P(new car) = 120/360 = 1/3
find the probability of the pointer landing on a new car
AD = 12 AE = 16 P(AD) = 12/16 = 3/4, 0.75, 75%
find the probability that a point K, selected randomly on AE is on AD. express your answer as a fraction, decimal, and percent.
BC = 6 AE = 16 P(BC) = 6/16 = 3/8, 0.375, 37.5%
find the probability that a point K, selected randomly on AE is on BC. express your answer as a fraction, decimal, and percent.
BD = 10 AE = 16 P(BD) = 10/16 = 5/8, 0.625, 62.5%
find the probability that a point K, selected randomly on AE is on BD. express your answer as a fraction, decimal, and percent.
CE = 8 AE = 16 P(CE) = 8/16 = 1/2, 0.5, 50%
find the probability that a point K, selected randomly on AE is on CE. express your answer as a fraction, decimal, and percent.
P = 2b + 2h
perimeter of a rectangle
P = 4s
perimeter of a square
m = (y₂-y₁) / (x₂-x₁)
slope formula
P = 34 if dimensions are tripled, the area is tripled too P = 3(34) = 102 inches
suppose the dimensions of a rectanlge with a perimeter of 34 inches are tripled. find the perimeter of the new rectangle in inches.
nonoverlapping
the area of a region is equal to the sum of the areas of its _______________________ parts (area addition postulate)
when one dimension is changed proportionally, the area changes the same way so the area is multiplied by 5
the base length of the triangle with vertices (1, 5), (2, 3), and (-1, -6) is multiplied by 5. describe the effect of change of the area.
apothem
the perpendicular distance from the center of a regular polygon to a side of the polygon
center of a circle
the point inside a circle that is the same distance from all the points on the circle
center of a regular polygon
the point that is equidistant from all vertices of the regular polygon.
original : r = 18 cm A = πr² A = π(18)² A = 324π radius x ¹/₃ r x ¹/₃ = 6 cm A = πr² A = π(6)² A = 36π 324π = (36π)x x = 9 the area was divided by 9
the radius of the circle is multiplied by ¹/₃. describe the effect on the change on the area.
circle
the set of all points in a plane that are a fixed distance from a given point called the center of the circle
*c = one side of square* 4² + 4² = c² √32 = √c² c = 4√2 P = 4(4√2) = 16√2) P ≈ 22.63m A = (4√2)² = 4√2 x 4√2 = 16 × 2 A = 32m²
the vertices of the inside square are the midpoints of the sides of a larger square. find the perimeter and the area of the inside square. round to the nearest hundredth.
C of small = πx C of large = π(x + 10) large-small = 3.14(x + 10) - 3.14x = 3.14x + 31.40 - 3.14x = 31.40 units
two circles have the same center. the radius of the larger circle is 5 units longer than the radius of the smaller circle. find the difference in the circumferences of the two circles. round to the nearest hundredth.
*triangle at point, rectanlge in middle, semicircle on rounded end* A of ∆ = ½(2)(2) = 2 ft² A of ½ circle = ½π(1.5)² ≈ 3.53 ft² A of rect. = (3)(2) = 6 ft² A ≈ 12 ft²
use a composite figure to estimate the shaded area. the grid had squares with side lengths of 1 ft.
P(SUV hits box) = interval for collision/interval where box may fall = 20/60 = 1/3
when a certain SUV travels at 30mph, it has a stopping distance of 40 ft. if a cardboard box falls off a truck between 20 to 80 feet in front of this SUV, what is the probability that the SUV will hit the box?
A of rect = 24(36) = 864 cm² A of 1st sq = ¹/₁₂(864) = 72 cm² side of sq = √72 = 6√2 cm A of 2nd sq = ³/₄(864) = 648 cm² side of sq = √648 = 18√2 cm
you are designing a target that is a square inside a 24 cm by 36 cm rectangle. what is the length of the side of the square if the target has a probability of ¹/₁₂? what is the length of a side of the square if the target has a probability of ³/₄?
