 Parallelogram and Triangles

Can you tell me what is the shape of your book cover or your laptop screen? Yes, it is a parallelogram. Most of the roofs of the houses are parallelogram in shape. Let us now study about the area and perimeter of parallelogram and triangles in detail.

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What does ‘parallel lines’ mean? Parallel lines are the two lines that never meet. A parallelogram is a slanted rectangle with the length of the opposite sides being equal just like a rectangle. Because of the parallel lines, opposite sides are equal and parallel. Suppose if every pair of opposite sides of a quadrilateral is equal, then it becomes a parallelogram. Diagonals of a parallelogram bisect each other. So, when the diagonals of a parallelogram bisect each other, it divides it into two congruent triangles. In a parallelogram, the angles are not right angles. The sum of the angles of a parallelogram is 360°. The area of and perimeter of parallelogram is given by (where b = base length, a = adjacent side length and h = height from the base to the opposite side):

Area of Parallelogram= b×h

Perimeter of Parallelogram = 2(a+b)

Properties of Parallelogram

• Opposite sides are congruent, AB = DC
• Opposite angles are congruent D = B
• If one angle is right, then all angles are right.
• The diagonals of a parallelogram bisect each other.

Triangles

When you think of drawing a hut, you draw a triangle having three sides. The pizza when you cut it into equal four pieces you get each part in triangular shape. Triangles are basic shapes that we come across in our day to day life. A triangle is a simple closed curve or polygon which is created by three line-segments. In geometry, any three points, specifically non-collinear, form a unique triangle and separately, a unique plane (known as two-dimensional Euclidean space). The basic elements of the triangle are sides, angles and vertices. Classification triangles based on angles are namely:

• Acute Triangle: This is a triangle in which each of the angles is acute and measure is less than 90°
• Right Angled Triangle: It is a form of a triangle wherein one particular angle is a right angle
• Obtuse Triangle: Triangle in which one of the angles stays obtuse is called as an obtuse triangle.

Further, triangles can be classified depending on the number of congruent sides that means the side length. Therefore, you can count on two different ways to classify the types of triangle:

1. Scalene, meaning that every side length in a triangle is different.
2. Equilateral means that every side length in a triangle is similar.
3. The isosceles triangle means, at least two of the triangle side lengths are similar.

Area of a Triangle

To find the area of a triangle you need 2 things: the base and the height. The height of the triangle is the perpendicular drawn on the base of the triangle. Area of the triangle is calculated by the formula

Area of a Triangle = 1/2 × base × height

Solved Examples For You

Q1. The base and the corresponding altitude of a parallelogram are 10 cm and 3.5 cm respectively. The area of the parallelogram is:

1. 30  cm²
2. 35  cm²
3. 70  cm²
4. 17.5 cm²

Solution: B. The area of parallelogram is given by, base × height cm². Therefore, the area of the given parallelogram = 10 × 3.5 = 35 cm²

Q2. The hypotenuse of a right-angled isosceles triangle is 5 cm The area of the triangle is:

1. 5 cm²
2. 6.25 cm²
3. 6.5 cm²
4. 12.5 cm²

Solution: B. Let the two sides be a² + a² = 25
2a² = 25
a² = 12.5

Area of a triangle = 1/2× a × a = a²/2
= 12.5/2
= 6.25 cm²

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