Area of Trapezium by Finding the Area of a Triangle of Same Area

Q.

The area of a trapezium is 384 $c{m}^2$.Its parallel sides are in the ratio 3:5 and the perpendicular distance between them is 12 cm.Find the length of each of the parallel sides.

Q.

Question 19

The perimeter of a trapezium is 52 cm and its each non-parallel side is equal to 10 cm with its height 8 cm. Its area is

$\left(a\right)124c{m}^2$
$\left(b\right)118c{m}^2$
$\left(c\right)128c{m}^2$
$\left(d\right)112c{m}^2$

Q.

The cross-section of a canal is a trapezium in shape.If the canal is 10 m wide at the top 6 m wide at the bottom, and the area of the cross-section is 72 $m^2$, determine its depth.

Q.

Find the altitude of a trapezium whose area is 65 $c{m}^2$ and whose bases are 13 cm and 26 cm.

Q.

Question 40

A trapezium with 3 equal sides and one side double the equal side, can be divided into ___ equilateral triangles of ___ area.

Q.

Find the area of a trapezium whose parallel sides are 25 cm, 13 cm and other sides are 15 cm each.

Q.

Top surface of a table is trapezium in shape.Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.

Q.

The area of a rhombus is equal to the area of triangle whose base and the corresponding altitude are 24.8 cm and 16.5 cm respectively.If one of the diagonals of the rhombus is 22 cm, find the length of the other diagonal.

Q.

In exchange of a square plot one of whose sides is 84 m, a man wants to buy a rectangular plot 144 m long and of the same area as of the square plot.Find the width of the rectangular plot.

Q.

Find the area of the field shown in the figure by dividing it into a square rectangle and a trapezium.

Q.

Find the sum of the lengths of the bases trapezium whose area is 4.2 $m^2$ and whose height is 280 cm.

Q.

If the area of a trapezium is 28 $c{m}^2$ and one of its parallel sides is 6 cm, find the other parallel side if its altitude is 4 cm.

Q.

There is a pentagonal shaped park as shown in the figure. Jyoti and Kavita divided it in two different ways.

Find the area of this park using both ways. Can you suggest another way of finding its area?

Q. Question 1
The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are
1 m and 1.2 m and the perpendicular distance between them is 0.8 m.

Q.

The area of a trapezium-shaped field is 600 m², the distance between two parallel sides is 15m and one of the parallel sides is 20 m. Find the other parallel side.

1. 40m

2. 50m

3. 60m

4. 70m

Q.

Find the area of trapezium whose parallel sides are of length 16 dm and 22 dm and whose height is 12 dm.

Q.

A trapezium with $3$ equal sides and one side double the equal side can be divided into __________ equilateral triangles of _______ area.

Q.

The area of a trapezium is 91 $c{m}^2$ and its height is 7 cm.If one of the parallel sides is longer than the other by 8 cm, find the two parallel sides.

Q.

Find the area of trapezium with base 15 cm and height 8 cm.If the side parallel to the given base is 9 cm long.

Q.

The area of trapezium is 1586 $c{m}^2$ and the distance between the parallel sides is 26 cm.If one of the parallel sides is 38 cm, find the other.

Q.

Find the area, in square metres, of the trapezium whose bases and altitude area as under:

(i) bases=12 dm and 20 dm, altitude=10 dm

(ii) bases=28 cm and 3 dm, altitude=25 cm

(iii) bases=8 m and 60 dm, altitude=40 dm

(iv) bases=150 cm and 30 dm, altitude=9 dm

Q.

Four points A, B, C, D are given on circle. Line segment AB and CD are parallel. Find the area of the figure formed by these points.

1. 98 cm${}^2$

2. 7 cm${}^2$

3. 49 cm${}^2$

4. 28 cm${}^2$

Q. The height of the trapezium having area as 36cm2 and parallel side as 10 cm and 8 cm is

1. 2 cm
2. 4 cm
3. 6 cm
4. 8 cm

Q.

The perimeter of the rectangle is $480cm$ and its length is $140cm$. Find its area in square metres.

Q.

A quadrilateral has an area of 453.6 $c{m}^2$. The length of a diagonal is 42 cm and the perpendicular distance from one vertex is 10 cm. Find the perpendicular distance from the other vertex (in cm). ___​

Q.

Find the area of a rhombus whose side is $5cm$ and whose altitude is $4.8cm$. If one of its diagonal is $8cm$ long find the length of the other diagonal.

Q.

Mohan wants to buy a trapezium shaped field.Its side along the river is parallel and twice the side along the road.If the area of this field is 10500 $m^2$ and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

Q.

The side of a regular hexagon with perimeter 84 cm is:

1. 28 cm

2. 7 cm

3. 14 cm

4. 21 cm

Q.

The area of a rectangle is $40{\mathrm{cm}}^2$. If its length is $\left(2\mathrm{k}-5\right)\mathrm{cm}$ and its breadth is $8\mathrm{cm}$. Then, find the value of $\mathrm{k}$.

Q. The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.