Transcription

1 Types of Triangle Sum of internal angles of triangle = 80 Equilateral Δ: All sides are equal Each internal angle = 60 Height divide the base into two equal parts Perimeter of triangle = 3 side Height of Δ = 3 side 3 Area of Δ= side Isosceles Triangle: Two sides one equal Height opposite to equal sides are equal Height divide the base into two equal parts Perimeter of Δ = sum of sides Area of Δ= base height Scalene Triangle: No two sides are equal No two angles are equal Perimeters of triangle = sum of side = a + b + c a+ b+ c where S = and a, b, c are sides ( )( )( ) Area of Δ= s s a s b s c Right Angle Δ: h = P + b Perimeter = P + b + h Area = base height AREAS = P b Sum of internal angles of a quadrilateral = 360

2 Squre: All sides are equal Each angle = 90 Equal diagonals bisect Each other at 90 Perimeter of square = side Diagonal of square = Area of square = side = ( diagonal) side Rectangle: Opposite sides are equal and parallel Each integral angle = 90 Diagonals are equal Perimeter of Rectangle = (length + breadth) Areas of Rectangle = length breadth Rhombus: All sides or equal Unequal diagonals bisect each other at 90 Perimeter of Rhombus = side Areas of Rhombus = Pr oduct of diagonals Area of Rhombus = base height Parallelogram: Opposite sides are equal and parallel Sum of alternate angle of parallelogram = 80 Sum of all internal angles of a parallelogram = 360 Perimeter = sum of sides Area of parallelogram = base height Circle: Diameter of Circle = radius = r Circumference of circle = πr Area of circle = πr where π= Ring: Area of Ring = πr πr = π(r r ) r

3 Difference of circumference of circle = πr πr = π(r r) PROBLEMS. Ratio of angles of a triangle is 3 : 5 :. Find difference of twice the smallest angle and half the largest angle of triangle. ) 5 ) 30 3) ) 3 Ans: 3x + 5x + x = 80 5x = 80 x = Smallest angle = 3 = 36 Largest angle = = 8 Difference of twice the smallest angle and half the largest angle = 36 8 = = 30. Ratio of length and breadth of a rectangle is : 3. Perimeter of rectangle is cm. Find Area of rectangle. ) 65 cm ) 66 cm 3) 68 cm ) 8 cm Ans: 3 Perimeter = (x + 3x) = x = 8 Area of rectangle = l b = 3 = 68 cm 3. Ratio of angle a quadrilateral is : : 3 :. Find sum of twice the smallest angle and half of largest angle. ) ) 50 3) 56 ) 6 Ans: Smallest angle = 360 = 36 0 Largest angle = 360 = 0 Sum of twice the smallest angle and half of largest angle = + = = 36 +

4 . Circumference of a circle is 88 cm. Find its Area. ) 600 cm ) 66 cm 3) 65 cm ) 6 cm Ans: πr = r = = cm Area of circle = πr = 66 cm = 5. The perimeter of a square is equal to the perimeter of a rectangle of length 30 cm. The area of rectangle is 360 cm. What is the side of square. ) cm ) cm 3) cm ) 8 cm Ans: 360 breadth of rectangle = = cm 30 Perimeter of rectangle = (30 + ) = 8 cm Perimeter of square = 8 cm 8 Side of square = = cm 6. Diagonals of rhombus are cm and 8 cm respectively. Find Area of rhombus. ) 05 cm ) 08 cm 3) 0 cm ) 0 cm Ans: Area of Rhombus = d d 8 08cm = =. Diagonal of a square is 5. Find perimeter of square. ) 0 cm ) 5 cm 3) 50 cm ) 00 cm Ans: 5 Side of square = = 5 Perimeter = 5 = 00 cm

5 EXERCISE. Ratio of angle of triangle A is 3 : : 5 and ratio of angle of triangle B is 5 : 6 :. Find difference of largest angle of triangle A and smallest angle of triangle B. ) 0 ) 5 3) Length of rectangle is cm more than its breadth. Perimeter of rectangle is 6 cm. Find breadth of this rectangle. ) cm ) 6 cm 3) 8 cm ) 30 cm 3. Length of a rectangle is increased by 0% and its breadth decreases by 0%. What will be effect on its Area? ) 0% ) % 3) % ) 6%. Length of a square increases by 0% and its breadth decreases by 0%. Find ratio of Area of rectangle thus formed and area of square. ) : 5 ) 5 : 3) 0 : 5 ) 3 : 5. Area of circular jogging track is 3850m. What is the circumference of the jogging track. ) 5 metres ) metres 3) 0 metres ) 35 metres 6. The circumference of a circle is equal to the perimeter of a square. The side of the square is 33 cm. What is double the diameter of the circle?what ) cm ) cm 3) 0.5 cm ) 9 cm. Equal sides of an Isosceles triangle are 3 cm and other side is 0 cm. Find Area of triangle. ) 60 cm ) 50 cm 3) 0 cm ) 5 cm 8. What would be the area of a circle whose diameter is 35 cms? ) 96.5 sq. cms. ) 85.5 sq. cms. 3) 98.5 sq.cms. ) sq. cms. 9. The perimeter of a square is thrice the perimeter of a rectangle. If the perimeter of the square is 6 cms and the length of the rectangle is 8 cms. What is the difference between the breadth of the rectangle and the side of the square? ) 5 cms ) 9 cms 3) 0 cms ) 8 cms 0. A man riding a bicycle, completes one lap of a squre field along its perimeter at the speed of 3. km/hr in minute 0 seconds. What is the area of the field? ) 5900 sq. mts ) 5600 sq. mts 3) 800 sq. mts ) cannot be determined Answers ) ) 3 3) ) 5) 3 6) 3 ) 8) 9) 0) 3