# Square

## Trending Questions

**Q.**

The altitude of a right triangle is $7cm$ less than its base. If the hypotenuse is $13cm$, find the other two sides.

**Q.**

Explain how a square is. (i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle.

**Q.**

Question 70

The largest square that can be drawn in a circle has a side whose length is 0.707 times the diameter of the circle. By this rule, find the length of the side of such a square, when the diameter of the circle is

(a) 14..5 (b) 8.63

**Q.**

In the given figure, ABCD is a square and ∠PQR=90∘. If PB = QC = DR, prove that (i) QB = RC, (ii) PQ = QR, (iii) ∠QPR=45∘

**Q.**

Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area. [3 MARKS]

**Q.**

The figure formed by joining the mid-points of the adjacent sides of a square is a

square

rhombus

rectangle

parallelogram

**Q.**Question 4

In quadrilateral ABCD, ∠A+∠D=180∘ . What special name can be given to this quadrilateral?

**Q.**

Find which of the following are true:

1.All rhombuses are squares

2.All squares are rectangles

3.All rectangles are parallelograms

4.All parallelograms are quadrilaterals

5.All parallelograms are rhombuses

2, 3 and 4

only 1

1, 2 and 3

3, 4 and 5

**Q.**ABCD is a cyclic quadrilateral in which AC and BD are it's diagonals. Draw BC as base and AD as upper side respectively. If angle DBC=60 and angle BAC=30, find angle BCD.

**Q.**

Things which concide with one another are equal to one another. Tell it's meaning with proof to it....!.?..!?..

**Q.**

K, L, M and N are points on the sides AB, BC, CD and DA respectively of a square ABCD such that AK = BL = CM = DN. Prove that KLMN is a square.

**Q.**All squares are rectangles but all rectangles are not squares?

- True
- False

**Q.**

The measure of each angles of a convex quadrilateral is _______ $180\xb0$

**Q.**Question 15

ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.

**Q.**

A square field is of side $35m$. Find its perimeter and area in acres.

**Q.**

A metal box with a square base and vertical sides is to contain $1024c{m}^{3}$. The material for the top and bottom costs $\u20b95/c{m}^{2}$ and the material for the sides costs $\u20b92.50/c{m}^{2}$. Find the least cost of the box.

**Q.**

Match the following:

QuadrilateralProperties1. TrapeziumA) A parallelogram, where diagonals bisect at rightangles, all sides are equal and noneof the angles are equal to 90∘2. SquareB) A quadrilateral, where only one pairof opposite sides is parallel and unequal3. RectangleC) A parallelogram, where diagonals are equal, all sides equal and all the angles are 90∘4. RhombusD) A parallelogram, where diagonals andopposite sides are equal, and all the angles are 90∘

1 - B, 2 - C, 3 - D, 4 - A

1 - C, 2 - B, 3 - D, 4 - A

1 - C, 2 - B, 3 - A, 4 - D

1 - A, 2 - B, 3 - C, 4 - D

**Q.**In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa told Chameli, “I think ABCD is a square”. State whether Champa's statement is true or false.

- True
- False

**Q.**

Find the edge of a cube of volume equal to the volume of a cuboid of dimensions 24 cm × 12 cm × 6 cm

6 cm

24 cm

14 cm

12 cm

**Q.**

A parallelogram with equal sides and equal angles will be:

Rectangle

Square

rhombus

Trapezium

**Q.**

DA || DB || DC

DA > DB > DC

DA = DB = DC

DA < DB < DC

**Q.**

What is the area of a square in ${m}^{2}$ with perimeter $128cm?$

**Q.**Which of the following is not the property of a square?

- The diagonals of a square bisect each other at right angles.
- Each angle of a square is a right angle.
- The diagonals of a square are unequal.
- The sides of a square are equal.

**Q.**Which of the following have all sides equal?

- Parallelogram
- Trapezium
- Rectangle
- Square

**Q.**

ln $\u25b3\mathrm{ABC}$, $\mathrm{AD}\perp \mathrm{BC}$ and point $D$ lies on $BC$ such that $2\mathrm{BD}=3\mathrm{CD}$. Prove that $5{\mathrm{AB}}^{2}=5{\mathrm{AC}}^{2}+{\mathrm{BC}}^{2}$.

**Q.**If PQ and RS are two perpendicular diameters of a circle, then PQRS is a

- Rectangle
- Trapezium
- Square
- Rhombus but not a square

**Q.**

ABCD is a rectangle in which diagonal BD bisects ∠B. Then, ABCD is a square.

True

False

**Q.**

Which of the following set of angles are found in a set squares ?

30∘, 60∘, 90∘

20∘, 70∘, 90∘

75∘, 15∘, 90∘

45∘, 45∘, 90∘

**Q.**

In the figure, angle ABC = 65^{o} and angle ACB = 58^{o}, the measure of angle BDC is

68

^{o}57

^{o}90

^{o}45

^{o}

**Q.**

All squares are rectangles.

- True
- False