Questions and Answers
What is the formula for the area of a triangle?
What is the formula for the perimeter of a quadrilateral?
What is the formula for the volume of a cube?
What is the formula for the surface area of a sphere?
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What is the formula for the area of a sector of a circle?
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What is the formula for the volume of a cylinder?
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What does the tense of a verb indicate?
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Which of the following sentences is in the present perfect continuous tense?
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What is the function of the future perfect tense?
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Which of the following sentences is in the past perfect tense?
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What is the function of the conditional tense?
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Which of the following sentences is in the subjunctive mood?
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How many basic tenses are there in English grammar?
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What is the function of the present continuous tense?
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Study Notes
Mensuration Formulae
Perimeter and Area of Various Shapes
Triangle
- Perimeter:
P = a + b + cwherea,b, andcare side lengths - Area:
A = (b \* h) / 2wherebis base andhis height - Heron's Formula:
A = √(s(s-a)(s-b)(s-c))wheresis semi-perimeter (s = (a + b + c) / 2)
Quadrilateral
- Perimeter:
P = a + b + c + dwherea,b,c, anddare side lengths - Area:
A = (d \* h) / 2wheredis diagonal andhis height - Trapezium:
A = (1/2) \* (sum of parallel sides) \* height
Circle
- Circumference:
C = 2 \* π \* rwhereris radius - Area:
A = π \* r^2 - Sector:
A = (θ / 360) \* π \* r^2whereθis angle in degrees
Polygon
- Perimeter:
P = sum of side lengths - Area:
A = (n \* s^2) / (4 \* tan(π/n))wherenis number of sides andsis side length
Volume and Surface Area of 3D Shapes
Cube
- Volume:
V = s^3wheresis side length - Surface Area:
SA = 6 \* s^2
Cylinder
- Volume:
V = π \* r^2 \* hwhereris radius andhis height - Surface Area:
SA = 2 \* π \* r \* (r + h)
Sphere
- Volume:
V = (4/3) \* π \* r^3whereris radius - Surface Area:
SA = 4 \* π \* r^2
Mensuration Formulae
Perimeter and Area of Various Shapes
Triangle
- The perimeter of a triangle is the sum of its side lengths:
P = a + b + c - The area of a triangle can be calculated using base and height:
A = (b \* h) / 2 - Heron's Formula provides an alternative method for finding the area of a triangle:
A = √(s(s-a)(s-b)(s-c)), wheresis the semi-perimeter
Quadrilateral
- The perimeter of a quadrilateral is the sum of its side lengths:
P = a + b + c + d - The area of a quadrilateral can be calculated using diagonal and height:
A = (d \* h) / 2 - For a trapezium, the area can be found using the formula:
A = (1/2) \* (sum of parallel sides) \* height
Circle
- The circumference of a circle is proportional to its radius:
C = 2 \* π \* r - The area of a circle can be calculated using its radius:
A = π \* r^2 - The area of a sector can be found using the angle and radius:
A = (θ / 360) \* π \* r^2
Polygon
- The perimeter of a polygon is the sum of its side lengths:
P = sum of side lengths - The area of a polygon can be calculated using its number of sides and side length:
A = (n \* s^2) / (4 \* tan(π/n))
Volume and Surface Area of 3D Shapes
Cube
- The volume of a cube is proportional to the cube of its side length:
V = s^3 - The surface area of a cube is proportional to the square of its side length:
SA = 6 \* s^2
Cylinder
- The volume of a cylinder is proportional to the radius squared and height:
V = π \* r^2 \* h - The surface area of a cylinder is proportional to the radius and height:
SA = 2 \* π \* r \* (r + h)
Sphere
- The volume of a sphere is proportional to the cube of its radius:
V = (4/3) \* π \* r^3 - The surface area of a sphere is proportional to the square of its radius:
SA = 4 \* π \* r^2
Tense
Definition and Types
- Tense refers to the form of a verb that indicates when an action takes place
- There are 12 basic tenses in English grammar
Present Tense
- Describes an action that is happening now
- Formed using the base form of the verb
- Examples:
- I go to school every day (Simple present)
- I am studying for my exam (Present continuous)
- I have studied English for three years (Present perfect)
- I have been studying English for three years (Present perfect continuous)
Past Tense
- Describes an action that happened in the past
- Formed using the past form of the verb
- Examples:
- I went to the park yesterday (Simple past)
- I was studying at 9 pm (Past continuous)
- I had eaten dinner before I went to the park (Past perfect)
- I had been studying for three hours before I took a break (Past perfect continuous)
Future Tense
- Describes an action that will happen in the future
- Formed using the future form of the verb
- Examples:
- I will go to the party tonight (Simple future)
- I will be studying at 10 pm (Future continuous)
- I will have studied English for four years by next year (Future perfect)
- I will have been studying English for four years by next year (Future perfect continuous)
Other Tenses
Conditional Tense
- Used to describe hypothetical or uncertain situations
- Examples:
- If you heat ice, it melts (Zero conditional)
- If it rains, I will take an umbrella (First conditional)
- If I won the lottery, I would buy a house (Second conditional)
- If I had studied harder, I would have passed the exam (Third conditional)
Subjunctive Mood
- Used to express doubt, uncertainty, or possibility
- Examples:
- It is necessary that he be there
- I suggest that he take a break
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Description
This quiz covers the formulas for perimeter and area of triangles and quadrilaterals, including Heron's Formula.
