AREA OF TRIANGLES. What are the base and height of a triangle? The base can be any of the three sides. The height is the distance from the vertex (corner)

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Presentation transcript:

AREA OF TRIANGLES

What are the base and height of a triangle? The base can be any of the three sides. The height is the distance from the vertex (corner) that’s not part of the base to the line containing the base

How are triangles related to parallelograms? Every triangle is half of a parallelogram This means that two of the same triangle combine to form a parallelogram

How are the area formulas for triangles and parallelograms related? Since a triangle is half of a parallelogram, the area of a triangle is half of the area of the parallelogram with the same base and height Area of a triangle = ½×base×height A = ½×b×h or A =

Review: What is the area of this parallelogram? What is the area of this triangle? Area of parallelogram = base×height A = 8 cm × 5 cm A = 40 cm² The base is still 8 cm and the height is still 5 cm. But since a triangle is half of a parallelogram, the area should also be half as much Area of a triangle = ½×base×height A = ½ × 8 cm × 5 cm A = 20 cm²

What is the area of this triangle? A triangle has an area of 40 feet² and a base of 20 feet. What is its height? The height is 11 km so the base must be the side it hits, 10 km. A = ½ × 10 km × 11 km A = 5 km × 11 km A = 55 km² We know A = 40 feet² and b = 20 feet Substitute into A = ½×b×h: 40 feet² = ½×20 feet×h 40 feet² = 10 feet×h ÷10 feet 4 feet = h

Direct Station We will use the whiteboards to solve both types of triangle problems: if we are given the base and height and are trying to find the area, and if we are given the area and are trying to figure out either the base or the height

Collaborative Station: Tracing You will see for yourself that you can use 2 of any triangle to form a parallelogram. First, you will trace a triangle from a worksheet. Then you will rotate your paper and trace the triangle again so that they combine to form a parallelogram. Label the base and height for your tracings. Calculate both the area of the entire parallelogram and the area of just a single triangle.

Independent Station: ST Math You will begin ST Math’s unit on area and perimeter.