- Books Name
- class 7 Mathematics Book
- Publication
- ReginaTagebücher
- Course
- CBSE Class 7
- Subject
- Mathmatics
Combination problems on square, rectangle and triangle
Introduction to square, rectangle
Square is one of the most basic shapes. A square is a quadrilateral with four equal sides & four equal angles.
A rectangle is a quadrilateral with four right angles. In a rectangle, all the angles are equal (360°/4=90°). Furthermore, the opposite sides are parallel and equal, and diagonals bisect each other.
Special case of square
A convex quadrilateral is a square in special conditions as follows:
- A rectangle with two adjacent equal sides.
- A rhombus with a right angle, all angles equal, equal diagonals.
- A quadrilateral with four equal sides and four right angles makes a square.
- A parallelogram with one right angle and two adjacent equal sides makes a square.
- An isosceles trapezoid with equal diagonals, base angle equals.
- A Kite with two disjoint pairs of adjacent sides is equal.
Area, perimeter & diagonal of square, rectangle, triangle
Diagonals of a square: Diagonals of a square are equal in length, they bisect the angles, and they are the perpendicular bisectors of each other.
Length of the diagonal d=√(a²+a²)=√(2a²2)=a√2 units.
Where d denotes a diagonal of a square is equal to side length times square root of 2.
Diagonals of rectangle: A rectangle has two diagonals they are equal in length and intersect in the middle. The diagonal is the square root of (width squared + height squared).
Diagonal(d)= l2+b2−−−−−−√
Where l is the length of the rectangle.
Where b is the breadth of the rectangle.
Perimeter is the actual distance around a closed figure.
2. Perimeter of a regular polygon = Number of sides x Length of one side
3. Perimeter of a square = 4 x side
Perimeter of a triangle = AB + BC + CA (Sum of all sides of triangle)
Perimeter of a rectangle = 2 [length + breadth]
= 2(l+ b)
Types of triangle
Right angle triangle: A triangle where one of its interior angles is a right angle 90°.
Area:
Area(A)=1/2(b×h)
Thus, the height of the triangle h=Area×2/b
And, the base of triangle b=Area×2/h
Where h is denoted as height.
Where b is denoted as base.
The perimeter:
a²+b²=c²
a, b are the lengths of the other two sides.
Where c is the length of the hypotenuse.
Sides: The two sides that are not the hypotenuse makes the right angle.
Hypotenuse: The side opposite the right angle is called the hypotenuse. It will always be the longest side of a right triangle.
Isosceles triangle: A triangle which has two of its sides equal in length.
Area:
Area(A)=1/2(b×h)
Thus, the height of the triangle h=Area×2/b
And, the base of the triangle b=Area×2/h
Where h is denoted as height.
Where b is denoted as base.
Altitude h=√(a²−b²)/4
The perimeter:
P=2a+b
Where a is the lengths of the two equal sides.
Where b is the lengths of the other sides.
Equilateral triangle: A triangle which has all three of its sides equal in length.
Area:
Area(A)=√3/4s².
Where s² denotes sides of the triangle.
The perimeter:
Perimeter(P)=a+b+c or P=s+s+s.
a, b, c are the lengths of the three equal sides.
or
S is the lengths of the three equal sides.