Deck 6: Geometry

Question 1

Determine the value of angle $\theta$ .

Answer 1

$144^{\circ}$

Question 2

Determine the value of angle $\theta$ .

Answer 2

$46^{\circ}$

Question 3

Determine the value of angle $\theta$ .

Answer 3

$140.5^{\circ}$

Question 4

Determine the value of angles $A$ and $B$ .

Question 5

Determine the value of angles A and B.

Question 6

Determine the value of angle $A$ .

Question 7

Determine the value of angles $A, B, C, D, F, G$ , and $H$ .

Question 8

Determine the value of angles $A, B, C, D, E, F$ , and $G$ .

Question 9

Determine the value of angles $\angle 1$ through $\angle 8$ . Line $\mathrm{a} \| \mathrm{b}$ and $\mathrm{c} \| \mathrm{d}$ .

Question 10

Determine the lengths $C P, P Q$ , and $Q D$ , given that $A C\|M P\| N Q \| B D$ .

Question 11

Determine the value of angles $\angle 1$ through $\angle 9$ . Line $\mathrm{a} \| \mathrm{b}$ and $\mathrm{c} \| \mathrm{d}$ .

Question 12

Determine the value of angles $A$ and $B$ .

Question 13

Determine the value of angle $\theta$ .

Question 14

Determine the value of angle $\theta$ .

Question 15

Determine the value of angle $\theta$ .

Question 16

Determine the values of angles $A, B$ , and $C$ .

Question 17

Determine the value of angle $\theta$ .

Question 18

The perimeter of an equilateral triangle is $17.6 \mathrm{~mm}$ . What is its area?

Question 19

The area of an equilateral triangle is $15.5 \mathrm{~cm}^{2}$ . What is its side length?

Question 20

Find angle $A$ in a triangle if the other two interior angles are $76^{\circ}$ and $61^{\circ}$ .

Question 21

Find angle $A$ in a triangle if the other two exterior angles are $107^{\circ}$ and $123^{\circ}$ .

Question 22

One brand of solar collector can generate $12 \mathrm{~W} / \mathrm{m}^{2}$ . If one such collector is triangular in shape with base $3.75 \mathrm{~m}$ and altitude $5.55 \mathrm{~m}$ , how many watts of power can it generate?

Question 23

What is the purchase cost, to the nearest dollar, of a triangular piece of land with base $40.0 \mathrm{~m}$ and altitude $64.0 \mathrm{~m}$ if the price is $\$ 0.65 / \mathrm{m}^{2}$ ?

Question 24

Calculate the area of a triangle having sides of lengths $1.7 \mathrm{~cm}, 2.1 \mathrm{~cm}$ , and $2.8 \mathrm{~cm}$ .

Question 25

Determine the height of an equilateral triangle with a side $5.1 \mathrm{in}$ .

Question 26

The hypotenuse of an isosceles right-angled triangle is $14.5 \mathrm{~cm}$ long. Determine the lengths of the other two sides.

Question 27

The area of a regular hexagon (six equal sides and six equal angles) is $190.5 \mathrm{~cm}^{2}$ . Determine the length of its side.

Question 28

Find distance $W P$ , given that the two beams $W X$ and $Y Z$ are parallel.

Question 29

Determine distances AB and DF, given that $BC \| DF and AB \| FE$ .

Question 30

A pair of tongs has handles that are $35.4 \mathrm{~cm}$ long and jaws that are $5.62 \mathrm{~cm}$ long. How far apart must the ends of the handles be to pick up a piece of hot metal that is $2.99 \mathrm{~cm}$ wide?

Question 31

Determine the height of a tree if its shadow is $20.3 \mathrm{~m}$ long at same time that a one metre stick has a shadow $1.4 \mathrm{~m}$ long.

Question 32

Determine the missing lengths in this roof truss diagram with evenly spaced vertical posts:

Question 33

Determine the value of angles $A, B, C, D, E, F, G, H$ , and $J$ .

Question 34

Determine the lengths $A B$ and $B C$ , given that $A B \| M N$ .

Question 35

A person stands $0.35 \mathrm{~km}$ from the base of a tower. How many metres tall is the tower if the angle of elevation is $45^{\circ}$ ?

Question 36

The crane shown below has a horizontal beam $7.8 \mathrm{~m}$ long supported from a $13.2 \mathrm{~m}$ long vertical beam. Find the length $A B C$ of the cable.

Question 37

A pyramid has four congruent triangular faces, each having a base of $23 \overline{0} \mathrm{~m}$ . The peak of the pyramid is $147 \mathrm{~m}$ above the base. How many litres of paint are needed to cover the pyramid if one litre of paint can cover $10.0 \mathrm{~m}^{2}$ .

Question 38

A roof pitch triangle in a building plan is a right triangle drawn parallel to the roof. What is the height $h$ of the roof in this plan? Treat the numbers in the roof pitch triangle as exact numbers.

Question 39

A boat is $425 \mathrm{~m}$ out from shore at a point that is $1.00 \mathrm{~km}$ from a lighthouse on the shore. How many metres is the boat from the lighthouse?

Question 40

What is the length of a diagonal of a square whose side is $12.5 \mathrm{~cm}$ ?

Question 41

What is the area of a square whose diagonal is $24 \mathrm{~cm}$ ?

Question 42

Calculate the area of this parallelogram:

Question 43

Calculate the area of this trapezoid:

Question 44

Calculate the area of this trapezoid:

Question 45

Determine the area of this figure. Write your answer to the nearest whole number.

Question 46

Determine the area of this figure:

Question 47

What will it cost to pave a driveway that is $22 \mathrm{~m}$ long and $4.8 \mathrm{~m}$ wide if the price is $\$ 0.15 / \mathrm{m}^{2}$ ?

Question 48

What will it cost to carpet a rectangular floor that is $3.2 \mathrm{~m}$ by $5.5 \mathrm{~m}$ at $\$ 4.80$ per square metre?

Question 49

The area of a trapezoid is $1.26 \mathrm{~m}^{2}$ . Determine the length of its height and two bases if the lower base is equal to the height and the upper base is three-quarters of the lower base.

Question 50

A skyscraper is $258.0 \mathrm{~m}$ high with a rectangular base measuring $32.0 \mathrm{~m}$ by $28.0 \mathrm{~m}$ . The exterior walls of the building, except for the window supports, are covered with glass. What is the cost of glass for this building if the window supports take up $12500 \mathrm{~m}^{2}$ and the glass costs $\$ 10.50 / \mathrm{m}^{2}$ ?

Question 51

A kite frame is made in the shape of a rhombus where one of the angles is $135^{\circ}$ . It is covered by 2912 $\mathrm{cm}^{2}$ of fabric. What is the side length of the kite?

Question 52

A building near the docks in Hamburg, Germany has a cross-section in the shape of a parallelogram with base $86.0 \mathrm{~m}$ and height $20.9 \mathrm{~m}$ . What is the area of the cross-section?

Question 53

The diameter of a circle is $4.0 \mathrm{~cm}$ less than the circumference. What is the radius?

Question 54

Two circles have the same centre, but one circle has a radius $2.0 \mathrm{~cm}$ greater than the other. The area of the inner circle is $14 \mathrm{~cm}^{2}$ less than the area of the outer circle. What is the radius of the smaller circle?

Question 55

What is the circumference of a circular pond having an area of $22.9 \mathrm{~m}^{2}$ ?

Question 56

What is the area of a circle with a circumference of $34 \mathrm{~m}$ ?

Question 57

What is the diameter of a circle whose area is $784 \mathrm{~cm}^{2}$ .

Question 58

A manhole cover has an area of $4071.5 \mathrm{~cm}^{2}$ . What is the diameter?

Question 59

What is the area of the largest circle you can cut from a square sheet of metal with area $3.5 \mathrm{~m}^{2}$ ?

Question 60

Calculate the distance $x$ .

Question 61

Three equal circles with radius of $25.0 \mathrm{~cm}$ each are touching each other from outside. Determine the area they enclose.

Question 62

When a circle is removed from the centre of a larger circle, the area is halved. Determine the radius of the larger circle if the radius of the smaller circle is $1.414 \mathrm{~cm}$ .

Question 63

The interior diameter of a building with a circular base is $23 \mathrm{~m}$ . The wall is $0.8 \mathrm{~m}$ thick. Determine the area occupied by the wall.

Question 64

If distance $A B$ is 1.6 units and distance $A C$ is 2.1 units, calculate the radius of the circle.

Question 65

An underground water main chamber has a concrete cover in the shape of a circle with a rectangle cut out for access. Calculate the cross-sectional area of the cover.

Question 66

Determine the area of the cross-section of a pipe which can carry as much water as two pipes with diameters $1.7 \mathrm{~m}$ and $1.5 \mathrm{~m}$ , respectively.

Question 67

Determine the radius of the cross-section of a pipe which can carry as much water as two pipes with diameters $2.50 \mathrm{~m}$ and $1.50 \mathrm{~m}$ , respectively.

Question 68

A parallelogram with a side length of 9.1 inches is inscribed inside a circle of diameter 14 inches, as shown. Determine the area of the shaded region.

Question 69

What is the area of the largest square that fits inside a circle of radius $3.50 \mathrm{~mm}$ ?

Question 70

Determine the length of $A B$ if the diameter of the circle is $60.0 \mathrm{~cm}$ .

Question 71

Determine the length of $B C$ if the diameter of the circle is $60.0 \mathrm{~cm}$ .

Question 72

A pulley is suspended from the ceiling by a string $30.2 \mathrm{~cm}$ long. The distance from the ceiling to the pulley is $13.7 \mathrm{~cm}$ . Determine the diameter of the pulley.

Question 73

Determine the length of belt required to connect two pulleys with diameters $35 \mathrm{~cm}$ and $75 \mathrm{~cm}$ , as shown below.

Question 74

The surface area of a cube is twice its volume (disregarding units). What is the side length of the cube?

Question 75

A company in British Columbia manufactures spherical tree houses. One model has an outside diameter of $3.20 \mathrm{~m}$ and is made from made of fibreglass that is $3.00 \mathrm{~mm}$ thick. The fibreglass is lined on the inside with wood $18.0 \mathrm{~mm}$ thick. What is the volume of living space inside the sphere in $\mathrm{m}^{3}$ ?

Question 76

An engineer designed a $620 \mathrm{ft}$ . long canal to have a trapezoid cross-section $8.0 \mathrm{ft}$ . deep and $14 \mathrm{ft}$ . across the bottom, with walls sloping outward at an angle of $30^{\circ}$ . A contractor placed a bid to excavate the canal at $\$ 1.75$ /cubic yard plus $10 \%$ profit. What was the bid, to the nearest dollar?

Question 77

A right prism has a base in the shape of a right isosceles triangle with hypotenuse measuring $8.5 \mathrm{~cm}$ . The height of the prism is $12 \mathrm{~cm}$ .
(a) What is the volume?
(b) What is the total surface area?

Question 78

A rectangular swimming pool is $8.0 \mathrm{~m}$ long. Each cubic metre of water added to the pool increases the depth by $32 \mathrm{~mm}$ .
(a) What is the width of the pool?
(b) How much water is needed to fill the pool to a depth of $2.3 \mathrm{~m}$ ?

Question 79

A spherical tank of radius $16.75 \mathrm{~m}$ is used for storing liquefied natural gas. What is the volume of the gas that it can store in cubic metres?

Question 80

A heavy external coating of insulation on the surface of a spherical tank enables the temperature of the liquefied natural gas stored inside to be maintained at a temperature of $-165^{\circ} \mathrm{C}$ . How many square metres of insulation are needed for a sphere of radius $36.3 \mathrm{~m}$ ?