#### If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram.

If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram.

#### The area of a right-angled triangle with a base of 10 cm and height of 5cm is

Area = 1 /2 × b × h = 1 /2 × 10 × 5 = 25 cm^{2} Hence, the required area is 25 cm^{2}

#### The base of a parallelogram is 18 cm and its distance from the opposite side is 8 cm, then its area is ____.

Let b = 18 cm and h = 8 cm We know that, Area of the parallelogram = b × h = 18 × 8 = 144 cm^{2} Hence, the required area is 144 cm^{2}.

#### A one rupee coin and 50 paise coin placed one on top of the other are congruent.

A one rupee coin and 50 paise coin placed one on top of the other are not congruent because they have the same shape but not the same size.

#### If the two perpendicular sides of a right angled triangle are in the ratio 3:4 and its area is 96 cm2, then its sides are ____.

Let the sides be 3x cm and 4x cm. Given A=96 cm^{2} We know that, A=1 /2 × b × h ⇒96=12×3x×4x ⇒192=12 x^{2} ⇒ x^{2}=16 ⇒x=4 (∵ x cannot be negative) 3x = 3 × 4 = 12 cm 4x = 4 × 4 = 16 cm Hence, the required sides are 12 cm and 16 cm.

#### Parallelograms on the same base and between the same parallel lines are equal in area.

Parallelograms on the same base and between the same parallel lines are equal in area.

#### The area of a parallelogram with base of 12 cm and height of 5 cm is ____ cm^{2}.

Given, base of the parallelogram = b = 12 cm and height = h = 5 cm Area of the parallelogram = b × h = 12 × 5 = 60 cm^{2} Hence, the required area is 60 cm^{2}.

#### The area of a parallelogram is 300 sq. cm and the height is 20 cm. Then its breadth is ____.

Let the breadth of the parallelogram be 'b' cm. Given, area of the parallelogram = A = 300 sq. cm and height = h = 20 cm Area of the parallelogram = b × h ⇒ 300 = 20 × h ⇒ b = 300 /20 ⇒ b = 15 cm Hence, the breadth of the parallelogram is 15 cm.

#### Two figures having same areas are not always congruent.

Two figures are congruent if they have same shape and size but not same areas.