Exploring the Area of a Triangle Formula

The video tutorial explains the formula for finding the area of a triangle, which is 1/2 base times height. It begins by comparing the formula to that of a rectangle and parallelogram, showing how the area of a triangle is derived from these shapes. The tutorial uses visual aids to demonstrate how two congruent triangles form a rectangle, thus explaining the 1/2 factor in the formula. It also covers how the formula applies to triangles without right angles by forming a parallelogram. The video aims to provide a comprehensive understanding of the triangle area formula and its derivation.

What is the formula for calculating the area of a triangle?

• Area = length × width

• Area = 1/2 base × height

• Area = 2 × base × height

• Area = base × height

How is the area of a rectangle related to the area of a triangle?

• The area of a triangle is half the area of a rectangle formed by two identical triangles.

• The area of a rectangle is the same as the area of a triangle.

• The area of a triangle is double the area of a rectangle.

• There is no relation.

How can the area of a parallelogram help in understanding the area of a triangle?

• The area of a parallelogram is twice the area of a triangle.

• Half the area of a parallelogram is equal to the area of a triangle.

• There is no connection.

• The area of a triangle is the same as the area of a parallelogram.

How does rearranging parts of a parallelogram demonstrate its area?

• By doubling the area.

• By forming a rectangle with the same area.

• By halving the area.

• By converting it into a circle.

What shape is formed when two congruent triangles are placed hypotenuse to hypotenuse?

• A rectangle

• A circle

• A square

• A parallelogram

Why is the formula for the area of a triangle half the product of its base and height?

• Because it always contains a right angle.

• Because the base is always longer than the height.

• Because it has three sides.

• Because a triangle is half of a rectangle.

What is the area of a right triangle with a base of 10 inches and a height of 8 inches?

• 40 square inches

• 80 square inches

• 18 square inches

• 20 square inches

Can the formula for the area of a triangle be applied to triangles without right angles?

• No, it only applies to equilateral triangles.

• Yes, it applies to all triangles.

• No, it only applies to right-angled triangles.

• Yes, but only if the triangle is isosceles.

What geometric shape is formed by copying and rotating a triangle?

• A parallelogram

• A square

• A circle

• A rectangle

Why do we use the formula '1/2 base × height' for the area of a triangle?

• Because it represents half of a parallelogram's area.

• Due to the triangle's three sides.

• Because it simplifies the calculation.

• To account for the triangle's angles.