- Area of figure
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- Properties of Area
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- Figure on the same base and between same parallels
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- Parallelogram on same base and between same parallel
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- Area of Parallelogram
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- How to solve the Area problem
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- Triangles and Parallelogram
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- Area of Triangle
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- How the Parallelogram area is calculated

a) Concepts questions

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

Which of the following figures lie on the same base and between the same parallels?

In such a case, write the common base and the two parallel

a) True. With Base BC and between parallel AD and BC, Triangle QBC and parallelogram ABCD

b) True. With base DC or AB and between parallel DC and AB, triangles are present

c) True. Same as above

d) False

e) True. Same as a

f) False

g) True

(a) If two triangles area are same areas, they will be congruent

(b) Two triangles having the same base (or equal bases) and equal areas lie between the same parallels.

(c) The area of a triangle is equal to the product of any of its side and any altitude

(d) The median of the triangles divides the triangle into two triangles of equal areas

(e) Parallelograms on the same base and between same parallels have same perimeter

(f) In a parallelogram, diagonals divide the parallelogram into four equal triangles

- False. Congruent triangles have equal areas but converse is not true
- True. Triangle area is (1/) X base X height. With same base and area, height should be equivalent, which means they lie on same parallel
- False. It is corresponding base and corresponding altitude
- True.
- False. Area is same but perimeter can be different
- True

PQRS is a rectangle with O as any point in its interior. If area (ΔPOS)= 4 cm

(a) 10cm

(b) 20cm

(c) 14 cm

(d) cm

Answer is (b)

$\frac{1}{2}PS \times (alitude)_{1}=4cm^{2}$

$\frac{1}{2}QR \times (alitude)_{2}=6cm^{2}$

Now PS=QR, So adding

$\frac{1}{2}PS \times [(alitude)_{1}+(altitude)_{2}]=10cm^{2}$

Now altitude

So area of rectangle=20 cm

In the below figure AD is the median, And E is any point on AD

Which of the following is true?

a) Area of triangle AEB= Area of triangle AEC

b) Area of triangle DEB= Area of triangle DEC

c) Area of triangle ABD= Area of triangle ADC

d) All the above

Since AD is median, it bisect the triangle is equal areas

So Area of triangle ABD= Area of triangle ADC ---(1)

Now ED is the median for EBC triangle

So Area of triangle DEB= Area of triangle DEC --(2)

Subtracting 1 and 2, we get

Area of triangle AEB= Area of triangle AEC

In the given figure ABCD is a parallelogram AE ⊥ DC and CF ⊥ AD. If AB = 18 cm, AE = 8 cm and CF = 16 cm, find AD.

a) 9 cm

b) 8 cm

c) 10 cm

d) None of the above

Parallelogram area= base X height

So DC×AE=AD×CF

Or AD=DC×AE/CF=9 cm

In the below figure AD is the median, and E is mid-point on AD. If the area of triangle is 16 cm

(a) 3cm

(b) 4cm

(c) 5 cm

(d) None of these

PQRS is a quadrilateral whose diagonal bisect each other at right angles

a) PQRS is a Square

b) PQRS is a rectangle

c) PQRS is a rhombus

d) None of these

In a quadrilateral ABCD, diagonal BD and AC intersect at point X

Which of the following is true?

(a) (Area of triangle BXC)×( Area of triangle AXD)=( Area of triangle AXB)×(Area of triangle CXD)

(b) (Area of triangle BXC)+( Area of triangle AXD)=( Area of triangle AXB)+(Area of triangle CXD)

(c) Insufficient information

(d) None of these

Hint, Draw perpendicular from A and C on BD and the calculate the area of each these piece and arranged them to get the solution

Two parallelograms are on the same base and between the same parellels. The ratio of their areas is:

a) 1:2

b) 1:1

c) 1:4

d) None of these

In a triangle A,B,C,D and E are such point BD=DE=EC

Which of the following is true?

a) Area of triangle ABD=Area of triangle ADE=Area of triangle AEC

b) Area of triangle ADE=(1/3) Area of triangle ABC

c) Triangle ABD is congruent to triangle AEC

d) None of the above

Hint: Draw perpendicular from A on BC and then calculate area for each of these triangle and you will find it same

Area of the triangle is 20 cm ^{2}, Area of rectangle is |
25cm^{2}. |

Area of the parallelogram is 100 cm^{2}. Both the Diagonal are drawn which cut the area into four pieces. The area of each piece is |
40cm^{2} |

In a triangle ABC,all the median intersect at point G, If the area of the triangle is 150 cm^{2},what is the area of the triangle AGC |
10 cm^{2} |

A trapezoid as parallel sides of 4 and 6 cm respectively, The altitude is 5 cm.A diagonal is drawn which cut the trapezoid into two traingles.Area of the triangle with base 4 cm is |
50 cm^{2} |

a) 40 cm

b) 25cm

c) 50 cm

d) 10 cm