Perimeter of Plane Figures

Q.

Find the perimeter of the given right-angled triangle.

1. 2 + $\sqrt{2}$ units

2. 2 units

3. 4 units

4. $\sqrt{2}$ units

Q.

Find the perimeter of the pentagon ABCDE.

1. 4 m

2. $3\sqrt{2}$ m

3. 6 m

4. $\sqrt{3}0$ m

Q.

The area of a square is 16 $m^2$. If the side of the square is equal to the side of an equilateral triangle, then find the perimeter of the triangle.
[2 MARKS]

Q.

The area of a triangle, with sides $a,b,c$ and semi-perimeter $s$, is:

1. √s(s-a)(s-b)(s-c)

2. √s(s+a)(s-b)(s-c)

3. √s(s-a)(s+b)(s-c)

4. √s(s-a)(s-b)(s+c)

Q.

What is the perimeter of the triangle ACD?

1. $1+\sqrt{2}+\sqrt{3}$ m

2. $2(1+\sqrt{2}+\sqrt{3})$ m

3. $3\sqrt{2}$

4. $2(\sqrt{2}+\sqrt{3})$ m

Q.

XYZ is an equilateral triangle and PQRS is a square. The figure has been cut and rearranged in the form of a trapezium.

What is the perimeter of the given trapezium ABEF? Take $\sqrt{2}$ = 1.4 and $\sqrt{3}$ = 1.7 (The triangle given is Equilateral)

1. 32 cm

2. 36 cm

3. 32.8 cm

4. 30.8 cm

Q.

If AB = 6 m, Find the Perimeter of the $△$ ADB.

1. 8 + $\sqrt{3}7$ m

2. 7 + $\sqrt{3}9$ m

3. 7 + $\sqrt{3}7$ m

4. 9 + $\sqrt{3}7$ m

Q.

What will be the Perimeter of the isosceles right-angled $△$ LON in the given figure?
(Given: KLOJ is a square)

1. $2\sqrt{2}$ + 1 cm

2. $\sqrt{2}$ + 1 cm

3. 2 + $\sqrt{2}$ cm

4. $\sqrt{2}$ cm

Q.

XYZ is an equilateral triangle and PQRS is a square. The figure has been cut and rearranged in the form of a trapezium.

What is the Perimeter of the rectangle ABCD? ( $△$ XYZ is equilateral )

1. 4(1 + $\sqrt{3}$) cm

2. 8(1 + $\sqrt{3}$) cm

3. 6(1 + $\sqrt{3}$) cm

4. 8(1 + $\sqrt{2}$) cm

Q.

If AB = 2 m, then find the perimeter of the $△$ ADB.

1. $2\sqrt{5}$ m

2. 2 + $\sqrt{5}$ m

3. 3 + $\sqrt{5}$ m

4. 4 + $\sqrt{5}$ m

Q.

The figure below shows a square, each of whose sides is 3 centimetres long. Each side is divided into three equal parts and these points are joined to form an octagon:

What is the perimeter of the octagon?

Q.

If AB = 6 m, then the perimeter of the $△$ ADB is .

1. $8+\sqrt{37}$ m
2. $7+\sqrt{37}$ m
3. $7+\sqrt{39}$ m

Q. The difference in perimeters of triangles ABC and ACD in the given figure ABCD is
( Take $\sqrt{2}$ = 1.4 and $\sqrt{5}$ = 2.2 )

1. 0.3 m
2. 0.6 m
3. 0.4 m

Q.

A square PQRS and an equilateral triangle XYZ are rearranged to form a figure as shown.

What is the perimeter of the ABDF ? (Take $\sqrt{2}$ = 1.4 and $\sqrt{3}$ = 1.7)

1. 25 cm

2. 31 cm

3. 24.4 cm

4. 32.4 cm

Q.

If CD = 9 m, then find the perimeter of the $△$ BCD.

1. $10+\sqrt{92}$ m

2. $10+\sqrt{82}$ m

3. $10+\sqrt{83}$ m

4. $11+\sqrt{82}$ m

Q.

What is the perimeter of the figure LORM? PQRS is a square. M and K are midpoints of the sides RQ and QP respectively.

1. $2\sqrt{2}$ cm

2. $4\sqrt{2}$ cm

3. $2\sqrt{2}$ + 1 cm

4. 2 + $\sqrt{2}$ cm

Q. In the given figure, a || gm ABCD and a rectangle ABEF are of equal area. Then,
(a) perimeter of ABCD = perimeter of ABEF
(b) perimeter of ABCD < perimeter of ABEF
(c) perimeter of ABCD > perimeter of ABEF
(d) perimeter of $ABCD=\frac{1}{2}(\mathrm{perimeter}\mathrm{of}ABEF)$

Q. The figure shown above consists a of square $BCDE$ and an equilateral triangle $\Delta ABE$. The length of $\overline{CD}$ is $6$ inches. Calculate the perimeter of $ABCDE$ in inches.

1. 18
2. 24
3. 30
4. 42
5. 45

Q. In fig. 9.11, $\square$ABCD is trapezium seg AD || seg BC
AB = 10, BP = 6, AD = 7, DC = 17.
Find BC and area of $\square$ABCD.

Q.

Find the Perimeter of the Square ADEC given in the figure.

1. 4

2. 4$\sqrt{2}$

3. 2$\sqrt{3}$

4. 2$\sqrt{2}$

Q.

What is the perimeter of the triangle ABC in the given figure ABCD? ( Take $\sqrt{2}$ = 1.4 )

1. 3.7 m

2. 3.8 m

3. 4.7 m

4. 4.8 m

Q.

What is the perimeter of the figure ACDE?

1. 8 + $4\sqrt{3}$ cm

2. 8 + $4\sqrt{2}$ cm

3. 16 + $4\sqrt{2}$ cm

4. 4 + $4\sqrt{2}$ cm

Q. What is the Perimeter of an equilateral triangle of side $\sqrt{4a^2+1+4a}$ units.

Q.

XYZ is an equilateral triangle and PQRS is a square. The figure has been cut and re-arranged in the form of a trapezium.

What is the length of the path ADCB in the trapezium ABEF?

1. 12 cm

2. 17 cm

3. 16 cm

4. 14 cm

Q. In $△$ ABC, AC$=5$, PC$=3$, and BP$=4\sqrt{3}$. What is the length of $\overline{AB}$?

Q.

What is the perimeter of the square ACEF?

1. $2\sqrt{2}$ units

2. 4 units

3. 2 units

4. $4\sqrt{2}$ units

Q. || gm ABCD and rectangle ABEF have the same base AB and are equal in areas. Show that the perimeter of the || gm is greater than that of the rectangle.

Q. In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.