Perimeter and Area of Triangles and Quadrilaterals

Perimeter is the distance around a closed figure.

Area is a quantity that expresses the extent of a two-dimensional surface or shape in a plane.

Perimeter of a triangle: It is the total length of all the sides of a triangle.

Perimeter of an equilateral triangle is three times the length of a side.

Area of a right-angled triangle is half of the product of its base and height.

Area of an equilateral triangle is the product of one fourth of square root of 3 and the square of the length of one side of this triangle.

A scalene triangle is a triangle with all three sides of unequal length.

In a right-angled triangle, the area of the square built upon the hypotenuse is equal to the sum of the areas of the squares built upon the remaining sides.

A parallelogram is a quadrilateral that has two pairs of parallel sides.

Trigonometric formulae are useful to calculate the area of the triangle when two sides and included angle are given.

An equilateral triangle is a triangle whose all the three sides are of equal length. In an equilateral triangle, all the three internal angles are of equal measure 60°.

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  • Q1

    The two sides and perimeter of triangle are 16 cm, 22 cm and 64 cm respectively, then the area of triangle (in cm2) is

    Marks:1
    Answer:

    3230.

    Explanation:

    Here a = 16 cm, b = 22 cm, let c = x cm

    Now perimeter = a + b + c
    64 = 16 + 22 + x
    x = 64 – 38
    x = 26 cm.
    S = (a + b + c)/2
    64/2 = 32 cm
    Area = s(s - a)(s - b)(s - c)
    = 32(32 - 16)(32 - 22)(32 - 26)
    = (32 x 16 x 10 x 6)
    = 3230 cm2

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  • Q2

    If the side of an equilateral triangle is ‘a’, then the area of equilateral triangle is

    Marks:1
    Answer:

    Explanation:

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  • Q3

    The perimeter of a triangular field is 240 dam. If two of its sides are 78 dam and 50 dam, then the area of triangular field (in dam2) is

    Marks:1
    Answer:

    1680

    Explanation:

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  • Q4

    Length of two equal sides ‘a’ and base ‘b’ of an isosceles triangle then the area of an isosceles triangle is

    Marks:1
    Answer:

    Explanation:

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  • Q5

    If base and height of a right triangle are ‘b’ and ‘h’ respectively, then the area of the triangle is

    Marks:1
    Answer:

    x b x h.

    Explanation:

    Area of a triangle = x b x h.

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