Perimeter of Square and Rectangle

Q.

$\Delta ABC$ is right-angled at $A$.$AD$ is perpendicular to $BC$, $AB=5cm,BC=13cm$and $AC=12cm$. Find the area of$\Delta ABC$. Also, find the length of$AD$.

Q.

The perimeter of a rectangle with length $8cm$ and breadth $10cm$ is $80cm.$

1. True
2. False

Q.

Find the perimeter of the rectangles whose length and breadth are given below:

length $25\mathrm{m}$ and breadth $10\mathrm{m}$

Q. ABCD is a rectangle in the diagram. P is a point on the side CD. Show that the area of ∆AQB is equal to the sum of the areas of ∆PQD and ∆PCB.

Q.

Find the perimeter of the following rectangles , if : length $=30\text{cm ,}$ breadth $=25\text{cm}$

Q. An umbrella is made by stitching $10$ triangular pieces of cloth of two different colours (see figure), each piece measuring $20cm,50cm$ and $50cm$. How much cloth of each colour is required for the umbrella?

Q. Let $S_1$, $S_2$, $S_3$, ... be squares such that for each $n\ge 1$, the length of a side of $S_n$ equals the length of a diagonal of $S_{n+1}$. If the length of a side of $S_1$ is 10 cm then for which of the following values of n is the area of $S_n$ less then 1$c{m}^2$

1. 7
2. 8
3. 9
4. 10

Q. The length and breadth of a rectangular courtyard is 45 m and 35 m respectively. Find the distance covered by a boy to take 5 rounds of the courtyard.

1. 800 m
2. 600 m
3. 200 m
4. 400 m

Q. The diagonal of a square is $4\sqrt{2}cm$. The diagonal of another square whose area is double that of the first square is :

1. 8 cm
2. $8\sqrt{2}cm$
3. $4\sqrt{2}cm$
4. 16 cm

Q. A triangular wall having sides 3 m, 5 m and 6 m has to be painted. If the cost of painting $1m^2$ of a wall is ₹5, what is the cost of painting the whole wall?
(Take $\sqrt{14}$ = 3.742)

Q.

The perimeter of a rectangle = 2[length + ________] [breadth/height]

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. If circle R, of area 4 square inches, radius of circle S is twice of circle R, then the area of circle S, in square inches, is

1. 8
2. $8\sqrt{2}$
3. 12
4. 16
5. $16\sqrt{2}$

Q. A square and an equilateral triangle have the same perimeter. If the diagonal of the square is $12\sqrt{2}$ cm, then the area of the triangle is:

1. $24\sqrt{2}c{m}^2$
2. $24\sqrt{3}c{m}^2$
3. $64\sqrt{3}c{m}^2$
4. $32\sqrt{3}c{m}^2$

Q. A design is made on a rectangular tile of dimensions 50 cm $\times$ 70 cm as shown in figure. The design shows 8 triangle, each of sides 26 cm, 17 cm and 25 cm. What's the total area of the design and the remaining area of the tiles.