Perimeter of the rectangle in the figure is 36 c e n t i m e t r e s . A C = 164 c e n t i m e t r e s . Find length of A B .

A B C D is a rectangle. Perimeter = 36 c m Diagonal A C = 164 = 41 × 4 = 2 41 c m . A B + B C = 36 / 2 = 18 ( A B + B C ) 2 = 18 2 A B 2 + B C 2 + 2 A B × B C = ( 20 - 2 ) 2 = 400 – 80 + 4 = 324 A B 2 + B C 2 = A C 2 = ( 164 ) 2 164 × 164 + 2 A B × B C = 324 2 A B × B C = 324 – 164 = 160 A B × B C = 80 ( A B - B C ) 2 = A B 2 + B C 2 – 2 A B × B C = 164 – 2 × 80 = 4 A B - B C = 2 A B + B C = 18 2 A B = 20 A B = 10 Hence, the required answer is 10 c m .

Perimeter of the rectangle in the figure is 36 c e n t i m e t r e s . A C = 164 c e n t i m e t r e s . What is A B + B C ?

Perimeter of the rectangle in the figure is 36 c e n t i m e t r e s . A C = 164 c e n t i m e t r e s . We have to find the length of A B + B C . A B C D rectangle. Perimeter = 36 c m Perimeter of a rectangle = 2 × l + b Perimeter = 2 × A B + B C ⇒ 2 × A B + B C = 36 A B + B C = 36 2 = 18 Hence, the required answer is 18 c m

Name the polygon. Make two more examples of this polygon.

The given figure is, The given polygon is a closed figure bounded by four sides. A closed polygon having 4 sides is known as a quadrilateral. Hence, the given polygon is a quadrilateral. Two more examples of Quadrilateral are Rectangle and Rhombus:

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A heptagon is also called a/an ___________.

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Important Questions on 2D - 3D Shapes

EASY

Mathematics>Geometry>2D - 3D Shapes>Polygons

In triangle $A B C, ∠ A = ∠ B = 30 °, A C = 4 c e n t i m e t r e s$ . What is the length of $B C$ ?

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EASY

Mathematics>Geometry>2D - 3D Shapes>Polygons

In the figure, $∠ B = 90 °, ∠ C = 44 °$

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What is the measure of $∠ A$ ?

EASY

Mathematics>Geometry>2D - 3D Shapes>Polygons

Perimeter of the rectangle in the figure is $36 c e n t i m e t r e s$ . $A C = \sqrt{164} c e n t i m e t r e s .$ Find length of $A B$ .

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MEDIUM

Mathematics>Geometry>2D - 3D Shapes>Polygons

The exterior angle of a regular polygon is

72 °

. What would be the sum of all its interior angles?

EASY

Mathematics>Geometry>2D - 3D Shapes>Polygons

Perimeter of the rectangle in the figure is $36 c e n t i m e t r e s$ . $A C = \sqrt{164} c e n t i m e t r e s .$ What is $A B + B C$ ?

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EASY

Mathematics>Geometry>2D - 3D Shapes>Polygons

If the interior angle of a regularpolygon is $108 °$ , then it is a-

1. Octagon

2. Hexagon

3. Pentagon

4. Tetragon

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Mathematics>Geometry>2D - 3D Shapes>Polygons

Identify the given geometrical figure. (Pentagon/Trapezium/Parallelogram/Rhombus)

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MEDIUM

Mathematics>Geometry>2D - 3D Shapes>Polygons

Examine the given figure and explain whether it is a polygon or not. (Yes/No)

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EASY

Mathematics>Geometry>2D - 3D Shapes>Polygons

Name the points where adjacent sides of polygon meet?

MEDIUM

Mathematics>Geometry>2D - 3D Shapes>Polygons

Name the diagonals of the following figure?
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EASY

Mathematics>Geometry>2D - 3D Shapes>Polygons

Examine whether the following figure is a polygon or not. If it is not, say why?

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MEDIUM

Mathematics>Geometry>2D - 3D Shapes>Polygons

A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.

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Mathematics>Geometry>2D - 3D Shapes>Polygons

Is an equilateral triangle a regular polygon? Write yes or no.

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Mathematics>Geometry>2D - 3D Shapes>Polygons

The given polygon is _____ (regular/ irregular) polygon.

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