Area of Triangle

Q.

The base of an isosceles right triangle is $30cm$its area is

Q. The base of an isosceles triangle is 6cm and it's perimeter is 16cm. Find the length of each of the equal sides.

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

Q.

In a right angled triangle if the base is 3 cm and perpendicular is 4 cm. What is the area of that triangle?

1. $8c{m}^2$

2. $6c{m}^2$

3. $7c{m}^2$

4. $9c{m}^2$

Q. The area of a triangle is 243$c{m}^2$ and its base and height are in the ratio 3:2.Find its base and height.

1. 9 cm, 6 cm
2. 15 cm, 10 cm
3. 18 cm, 12 cm
4. 27 cm, 18 cm

Q.

The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3:2. Find the area of the triangle.

1. $30\sqrt{2}c{m}^2$

2. $32\sqrt{2}c{m}^2$

3. $40\sqrt{2}c{m}^2$

4. $35\sqrt{2}c{m}^2$

Q. Find the area of $△$ABC, if BC = 10 cm and AD = 6 cm.

1. $15c{m}^2$
2. $20c{m}^2$
3. $25c{m}^2$
4. $30c{m}^2$

Q. Question 3
Length of the fence of a trapezium-shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.

Q. Areas of $△$ADC and $△$CDB are in ratio 3:2
and if AB = 10 cm and Area of $△$ABC is 20 $c{m}^2$, find the length of AD, BD.

1. 3 cm, 2 cm
2. 2 cm, 3 cm
3. 6 cm, 4 cm
4. 4 cm, 6 cm

Q. The height of a triangle is $x^4+y^4$ and its base is $14xy$. Find the area of the triangle. [1 mark]

Q.

A triangle with sides 12, 16 and 20 units is given.

Statement 1: To find the area of this triangle, the formula $Area=\frac{1}{2}\times base\times height$ is the ideal one to be used.

Statement 2: To find the area, the formula $Area=\sqrt{s(s-a)(s-b)(s-c)}$ is the ideal one to be used.

​Enter “1” if you feel Statement 1 is correct, or “2” if Statement 2 is correct.
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Q. In the given trapezium ABCE, perimeter of rectangle ABDE is 28 cm and its length is 8 cm and DC = 2 cm, then find the area of trapezium ABCE.

1. 24 $c{m}^2$
2. 48 $c{m}^2$
3. 54 $c{m}^2$
4. 72 $c{m}^2$

Q.

The sides of a triangle are $150\mathrm{cm},100\mathrm{cm}\mathrm{and}200\mathrm{cm}$. find the area of the triangle.

Q. Question 8
Mohan wants to buy a trapezium-shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is $10500m^2$ and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

Q.

ABCD is a rectangle such that

CD = 30 cm

BC = 40 cm

F is a point on the interior of the rectangle and the perpendicular from F meets the side AB at its midpoint i.e., E.

If EF = 32 cms.

Find the area of the region AFBCD [4 MARKS]

Q. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangles of base 8 cm and sides 6 cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it ?

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

Q. FInd the area of figure ABCDE.

Q. Match the following polygons to their respective area.

1. $sid{e}^2$
2. Length X Breadth
3. $\frac{1}{2}\times base\times height$
4. base$\times$height

Q. In the given figure, find the area of parallelogram ABCD, if the area of the shaded triangle is $9c{m}^2$

Q. Find the area of the shaded regions

1. $64c{m}^2$
2. $65c{m}^2$
3. $67c{m}^2$
4. $66c{m}^2$

Q. In given figure, BC = 6 cm and CD = 4 cm and perpendicular from point A to BD is of 5 cm length, then find the area of $△$ABD.

1. 15 $c{m}^2$
2. 20 $c{m}^2$
3. 25 $c{m}^2$
4. 30 $c{m}^2$

Q. ABCD is a parallelogram. P is any point on CD. If ar($△$DPA) = 35 $c{m}^2$ and ar($△$APC) = 15 $c{m}^2$, then area($△$APB) is

1. 50 $c{m}^2$
2. 15 $c{m}^2$
3. 70 $c{m}^2$
4. 35 $c{m}^2$

Q. Shyam wants to buy a trapezium shaped field in between a road and a river. Its side along the river is parallel to 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.

1. 140 m
2. 70 m
3. 100 m
4. 180 m

Q. A bathroom floor of area $120c{m}^2$ has to be refurnished with tiles. The shape of the tile is a triangle having the base as 3 cm and height as 4 cm. How many tiles are needed to refurnish the entire bathroom floor?

1. 20

Q. O is any point inside a rectangle ABCD. then $O{B}^2+O{D}^2=O{C}^2+O{A}^2$
If the above statement is true then mention answer as 1, else mention 0 if false

Q.

If the perimeter of a square is $16$cm, then its area is _ $c{m}^2$

Q. The area of an equilateral triangle is $49\sqrt{3}c{m}^2$. Taking each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circle. [ 4 MARKS ]

Q. Some measures are given in the adjacent figure, find the area of ABCD

Q. AD is median of $△ABC$ Area of $△AC$=15 $c{m}^2$ then area of $△ABC$ is

1. $22.5c{m}^2$
2. $15c{m}^2$
3. $30c{m}^2$
4. $10c{m}^2$

Q.