Area of Trapezium

Q. The perimeter of a triangle with sides 7 cm, 8 cm, 9 cm is ___ .

1. 21 cm
2. 22 cm
3. 24 cm
4. 23 cm

Q. Area of a trapezium is 16 $c{m}^2$. If the distance between parallel sides is 4 cm and one of the parallel side is 5 cm, find the length of other side.

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

Q. If sum of the parallel sides of a trapezium is 12 cm and height of the trapezium is 5 cm, find its area.

1. 17 $c{m}^2$
2. 30 $c{m}^2$
3. 34 $c{m}^2$
4. 60 $c{m}^2$

Q. Parallel sides of a trapezium are in the ratio 2:3 and if its height is half the length of smaller parallel side, then find the lengths of parallel sides if area of the trapezium is 40 $c{m}^2.$

1. 4 cm, 6 cm
2. 6 cm, 9 cm
3. 8 cm, 12 cm
4. 10 cm, 15 cm

Q. The doormat which is in a hexagonal shape has the following measures as given in the figure. Find its area.

1. $2560c{m}^2$
2. $3800c{m}^2$
3. $4580c{m}^2$
4. $5600c{m}^2$

Q. The area of the trapezium having parallel side as 27 cm and 13 cm and distance between them as 8 cm is

1. $130c{m}^2$
2. $320c{m}^2$
3. $160c{m}^2$
4. $180c{m}^2$

Q. If the parallel sides of a trapezium are in the ratio 4:5 and its height is 6 cm and its area is 54 $c{m}^2$, then find the lengths of parallel sides.

1. 4 cm, 5 cm
2. 16 cm, 20 cm
3. 8 cm, 10 cm
4. 12 cm, 15 cm

Q. In given frame (shaded region), the length and breadth of inner rectangle PQRS are 4 cm and 2 cm respectively, find the area of the frame if width of the frame is 2 cm throughout.

1. 24 $c{m}^2$
2. 32 $c{m}^2$
3. 40 $c{m}^2$
4. 48 $c{m}^2$

Q. In parallelogram ABCD, CD = 10 cm. Given that area of $△$BCE is 15 $c{m}^2$ and CF = 5 cm, then find the area of trapezium AECD.

1. 78 $c{m}^2$
2. 48 $c{m}^2$
3. 30 $c{m}^2$
4. 65 $c{m}^2$

Q. Fill in the blank:
In an isosceles trapezium, the non-parallel sides are __________ in length.

Q. Find the area of given figure, if AB = EF = 12 cm, CD = 10 cm and PQ = QR = 5 cm.

1. 55 $c{m}^2$
2. 60 $c{m}^2$
3. 110 $c{m}^2$
4. 220 $c{m}^2$

Q. What is the perimeter of a rectangle with dimensions 6 cm x 10 cm?

1. 30 cm
2. 32 cm
3. 34 cm
4. 36 cm

Q.

The areas of figure 1 (in $c{m}^2$​) and figure 2 (in $c{m}^2$​) are __ and __ respectively.

1. $41c{m}^2$, $41c{m}^2$
2. $31c{m}^2$, $35c{m}^2$
3. $21c{m}^2$, $21c{m}^2$
4. $11c{m}^2$, $10c{m}^2$

Q. In given hexagon, length of all sides equals to 6 cm, then find its area if AD = 12 cm, and PO = OQ = 5.2 cm.

1. 45 $c{m}^2$
2. 60 $c{m}^2$
3. 93.6 $c{m}^2$
4. 75.2 $c{m}^2$

Q. In a trapezium ABCD,
seg AB$||$ seg DC
seg BD$\perp$ seg AD,
seg AC$\perp$ seg BC,
If AD$=15$, BC$=15$ and AB$=25$. Find A$(\square$ ABCD$)$.

Q. Length of the fence of a trapezium shaped field $ABCD$ is $120m$. If $BC=48m$, $CD=17m$ and $AD=40m$. Side $AB$ is perpendicular to the parallel sides $AD$ and $BC$. Find the area of this field.

1. $660m^2$
2. $600m^2$
3. $630m^2$
4. $620m^2$

Q. Find the length of the parallel sides of a trapezium, which are in the ratio 1:2, if its height is 2 cm and area is 18$c{m}^2$.

1. 5 cm, 10 cm
2. 6 cm, 12 cm
3. 7 cm, 14 cm
4. 8 cm, 16 cm

Q. A straight pole has to be erected at a point on the outer boundary of a circular park having diameter 13 meters in such a way as that the differences of its distances from two diametrically opposite gates C and D fixed on the boundary in 7 meters. Is it possible to do so? If yes what is the sum of distances from the two gates should the straight pole be erected?

Q. In the given figure, $ABED$ is a parallelogram in which $AB=DE=10cm$ and the area of $△BEC$ is $72c{m}^2$. If $CE=16cm$, find the area of the trapezium $ABCD$

Q. In the given trapezium ABCE, ED = 10 cm, DC = 15 cm, find the length of AB, if area of $△$ADE is one-third of area of trapezium ABCD.

1. 6 cm
2. 2 cm
3. 4 cm
4. 5 cm

Q. Area of trapezium ABCE is 24 $c{m}^2$, find the length of AE if AB = 5 cm and CE = 7 cm.

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

Q. Find the area of given figures, if HI = 6, GF = 7, CD = 8, AB = 11, JF = DE = BC = CG = 2, GH = 4 in cm.

1. 45 $c{m}^2$
2. 54 $c{m}^2$
3. 66 $c{m}^2$
4. 78 $c{m}^2$

Q. The area of a trapezium with equal non parallel sides is $168m^2$. If the lengths of the parallel sides are 36 m and 20 m, find the length of the non-parallel sides.

1. 100 m
2. 0.1 km
3. 10 m
4. 0.001 km

Q.

If a trapezium ABCD has parallel side AB and CD measured 13 and 17 cm what should be the area of trapezium if the area of triangle ABC = 71$c{m}^2$.

1. 163.5

2. 205.5

3. 310

4. 91

Q. If we are using area of trapezium to find area of parallelogram then the parallel sides of trapezium are .

1. equal
2. different
3. non - parallel

Q. Length of parallel lines and heights of trapeziums are given respectively, then find their respective areas.

1. 9 $c{m}^2$
2. 10 $c{m}^2$
3. 16 $c{m}^2$
4. 18 $c{m}^2$

Q. If sum of the parallel sides of a trapezium is 12 cm and height of the trapezium is 5 cm, find its area.

1. 17 $c{m}^2$
2. 30 $c{m}^2$
3. 34 $c{m}^2$
4. 60 $c{m}^2$

Q. Which of the following options can be expressed as the area of given trapezium ABCF?

1. $\frac{1}{2}$$\times$(AB+CF)$\times$AE
2. $\frac{1}{2}$$\times$(AB+CF)$\times$BD
3. AB$\times$AE +
   $\frac{1}{2}$$\times$FE$\times$AE + $\frac{1}{2}$$\times$BD$\times$CD
4. AB$\times$CF

Q. The two non-parallel sides of isosceles trapezium are .

1. equal
2. non-equal
3. infinite

Q. In the given trapezium ABCE, ED = 10 cm, DC = 15 cm, find the length of AB, if area of $△$ADE is one-third of area of trapezium ABCD.

1. 2 cm
2. 4 cm
3. 5 cm
4. 6 cm