Math 6 Honors Periods 6 & 7 (Wednesday)

Areas of Triangles and Trapezoids 10-2

Any side of a triangle can be considered to be the base. The height is then the perpendicular distance from the opposite vertex to the base line.

Let us find the area of a triangle having base b and height h. The triangle and a congruent copy of it can be put together to form a parallelogram

Since the area of the parallelogram is bh—from yesterday’s lesson--the area of the triangle is half the area of the parallelogram so we have the following

Formula

Area of triangle = ½ · base · height

A = ½ bh

Find the area of each triangle

Look at the pictures in your textbook Page 325 and practice a few

Note that in the second example, the lengths of the sides of the right angle of the triangle were used as the base and the height. this can be done for any right triangle.

Trapezoids

The height of a trapezoid is the perpendicular distance between the parallel sides. These parallel sides are called the bases of the trapezoid. The method used to find the formula for the area of a triangle can be used to find the formula for the area of a trapezoid having bases b₁ and b₂ and height h. The trapezoid and a congruent copy of it can be put together to form a parallelogram. The area of the parallelogram is (b₁ + b₂)h and the area of the original trapezoid is half the area of the parallelogram.

Formula

Area of trapezoid = ½ · (sum of bases) · height

A = ½ (b₁ +b₂)h