Area of Triangles

Area of a triangle = ½(Base × Height)

Area of a parallelogram = Base × Height

The area of a triangle is half the area of a parallelogram on the same base and between
the same parallels.

Triangles on the same base and between the same parallels are equal in area.

A median divides a triangle into two triangles of equal area.

If a triangle and a parallelogram are on equal bases and between the same parallels, then the area of the triangle is half of the area of the parallelogram.

If two triangles are on the equal bases and between the same parallels, then they are equal in area.

The areas of triangles with the same vertex and bases along the same line are in the ratio of their bases.

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  • Q1

    In the following parallelogram ABCD, X and Y are the mid-points of AB and CD respectively. If the area of ADYX = 36 cm2, then the area of Δ BCD is equal to

    Marks:1
    Answer:

    36 cm2.

    Explanation:

    As X and Y are the mid-points of AB and CD.

    So, area of ADYX = 1/2 area of ABCD

    Since the area of a triangle is half the area of a parallelogram on the same base and between same parallels, we get

    area of DBCD = 1/2 area of ABCD

    Hence, area of DBCD = area of ADYX = 36 cm2.

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  • Q2

    If AD is a median of a triangle ABC and G is the mid-point of median AD, then ar(BGC) is equal to

    Marks:1
    Answer:

    2 ar( Δ AGC).

    Explanation:

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  • Q3

    In the following trapezium PQRS, if the area of POQ is 100 cm2, then the area of SOR (in cm2) is

    Marks:1
    Answer:

    100

    Explanation:

    Since triangle PQR and triangle QRS lie on the same base QR and between same parallel PS, therefore,

    area(PQR) = area (QRS) ...(1)

    On subtracting area (QOR) from both sides of equation (1), we get

    area (PQR) - area (QOR) = area (QRS) - area (QOR)

    area(POQ) = area(SOR)

    So, the area of SOR = 100 cm2

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  • Q4

    In a ΔABC, AD is the median. If area of ΔABD is 156 cm2, then the area of ΔADC (in cm2), is

    Marks:1
    Answer:

    156

    Explanation:

    AD is median of ABC.
    We know a median divides a triangle in two parts with equal areas.
    ar( ABD) = ar(ADC) Since ar(ABD) = 156 cm2, we get ar(ADC) = 156 cm2

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  • Q5

    P is any point lying on the side DC of a parallelogram ABCD. If the area of Δ APB is 125 cm2 and the side AB is 25 cm, then the distance between the sides AB and CD (in cm) is

    Marks:1
    Answer:

    10

    Explanation:

    ABCD is a parallelogram.

    ar(ABCD) = 2 ar(APB) [ar(APB) = 125 cm2)]

    (They lie on same base AB and in between same parallels AB and DC)

    ar(ABCD) = 2 x 125 cm2 = 250 cm2

    Also, ar(ABCD) = base x height [base AB = 25 cm]

    So, we have

    Height = ar(ABCD)/base = 250/25 = 10 cm

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