Question

Write the formulas of: rhombus, square, triangle, rectangle, right triangle, trapezium, cone, circle, semi circle, parallelogram, cylinder, cube, cone, cuboid, sphere, hemisphere

Answer 1

AREA AND PERIMETER OF SQUARE


Area of square = a²

Perimeter of square = 4a

here "a" stands for side length of square.

Examples problems on area of square

Examples problems on perimeter of square

Next we are going to see a formula for the next shape rectangle of the topic "area and perimeter formula for all shapes"

AREA AND PERIMETER OF RECTANGLE


Area of rectangle = L x W

Perimeter of rectangle = 2(l + w)

Here L and w represents length and width of rectangle.

Examples problems on area of rectangle

Examples of perimeter of rectangle

Next we are going to see a formula related to equilateral triangle of the topic area and perimeter formula for all shapes

AREA AND PERIMETER OF EQUILATERAL TRIANGLE

Area of Equilateral triangle = (√3/4) a²

Perimeter of Equilateral triangle = 3a

Here "a" represents side length of triangle.

Example problems on equilateral triangle

Next we are going to see a formula related to scalane triangle of the topic area and perimeter formula for all shapes

AREA AND PERIMETER OF SCALANE TRIANGLE



Area of scalene triangle = √s(s-a)(s-b)(s-c)

Perimeter of scalene triangle = a + b + c

here "s = (a + b + c)/2"

Example problems on scalene triangle

Next we are going to see a formula related to quadrilateral of the topic area and perimeter formula for all shapes

AREA AND PERIMETER OF QUADRILATERAL

Area of quadrilateral =(1/2) x d x (h₁+h₂)

Perimeter of quadrilateral = Sum of all four sides

Example problems of area of quadrilateral

Next we are going to see formula related to parallelogram of the topic area and perimeter formula for all shapes

AREA AND PERIMETER OF PARALLELOGRAM

Area of parallelogram = b x h

Perimeter of quadrilateral = Sum of all four sides

Example problems of area of parallelogram

Example problems of perimeter of parallelogram

AREA AND PERIMETER OF RHOMBUS

Area of rhombus =(1/2) x (d₁ x d₂)

Examples problems on area of rhombus

Examples problems on perimeter of rhombus

AREA AND PERIMETER OF TRAPEZIUM
Area of trapezoid =(1/2) (a + b) x h

Examples problems on area of trapezoid

AREA AND CICUMFERENCE OF CIRCLE

Area of circle = Π r ²

Circumference of circle = 2 Π r

Example problems of area of circle

Example problems of circumference of circle

AREA AND PERIMETER OF SEMI CIRCLE

Area of Semi circle= (1/2) Π r²

Perimeter of semi circle = (Π+2)r

Example problems on semi circle

AREA AND PERIMETER OF QUADRANT


Area of quadrant = (1/4) Π r²

Perimeter of quadrant = [(Π/2) + 2] r

Example problems on quadrant

AREA AND PERIMETER OF SECTOR

Area of the sector = (θ/360) x Π r ² square units

(or) Area of the sector = (1/2) x l r square units

Length of arc = (θ/360) x 2Πr

Perimeter of sector = L + 2r

Examples problems on area of sector

Examples problems on length of arc

Worksheet for length of arc

Perimeter of sector worksheets

Area of sector worksheet
AREA AND VOLUME OF CUBE

Curved surface area of cube = 4a²

Total surface area = 6a²

Volume of cube = a³
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Answer 2

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♦ CSA of cuboid ➾ 2(bh + hl)

♦ TSA of Cuboid ➾ 2(lb + bh + hl)

♦ Volume of Cuboid ➾ Length × Breadth × Height

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♦ CSA of cube ➾ 4L²

♦ TSA of Cube ➾ 6L²

♦ Volume of Cube ➾ Length³

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♦ CSA of  Right Circular Cylinder ➾ 2πrh

♦ TSA of  Right Circular Cylinder ➾ 2πr(r + h)

♦ Volume of  Right Circular Cylinder ➾ πr²h

♦ CSA of Right Circular Hollow Cylinder ➾ 2πh(r + R)

♦TSA of Right Circular Hollow Cylinder  ➾ 2π(r + R) (h + R – r)

♦  Volume of Right Circular Hollow Cylinder  ➾ πh(R² – r²)

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♦ CSA of Right Circular Cone ➾ πrl

♦ TSA of Right Circular Cone  ➾ πr(r + l)

♦ Volume of Right Circular Cone  ➾ ⅓ (πr²h)

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♦ CSA of Sphere ➾ 4πr²

♦ TSA of Sphere   ➾ 4πr²

♦ Volume of Sphere   ➾ 4/3 (πr²)

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♦ CSA of Hemisphere ➾ 2πr²

♦ TSA of  Hemisphere ➾ 3πr²

♦ Volume of  Hemisphere ➾ 2/3 (πr²)

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♦ CSA of Frustum ➾ πl(r + R)

♦ TSA of  Frustum  ➾ πl(r + R) + p(r² + R²)

♦ Volume of  Frustum  ➾ ⅓πh(r² + R² + rR)