Area of Triangles and Other Polygons

Recall that the area of a parallelogram is base x height.

If you divide a parallelogram into two congruent triangles, the area of each triangle is ½ x base x height.

parallelogramtotriangle.png

So the Area of a Triangle: A = ½ bh

In order to use the lengths of the legs of the triangle as the base and height, the legs must meet at a 90o angle.

Area of a Trapezoid

A trapezoid can be divided into a rectangle and two triangles.   The area of a trapezoid is the sum of the areas of the rectangle and the triangles.

areaoftrapezoid

So the Area of a Trapezoid is  

Steps

Calculate-the-Area-of-a-Trapezoid-Step-1-Version-2

Identify the length of both bases. The bases are the two parallel sides of the trapezoid. Let’s call them sides a and b. Side a is 8 cm long and side b is 13 cm long.
Calculate-the-Area-of-a-Trapezoid-Step-2-Version-2

Add the lengths of the bases. Add 8 cm and 13 cm. 8 cm + 13 cm = 21 cm.
Calculate-the-Area-of-a-Trapezoid-Step-3-Version-2

Identify the height of the trapezoid. The height of the trapezoid is perpendicular to the bases. In this example, the height of the trapezoid is 7 cm.
Calculate-the-Area-of-a-Trapezoid-Step-4-Version-2

Multiply the sum of the lengths of the bases by the height. The sum of the lengths of the bases is 21 cm and the height is 7 cm. 21 cm x 7 cm = 147 cm2.
Calculate-the-Area-of-a-Trapezoid-Step-5-Version-2

Divide the result by two. Divide 147 cm2 by 2 to get the final answer. 147 cm2/2 = 73.5 cm2. The area of the trapezoid is 73.5. You have just followed the formula for finding the area of a trapezoid, which is [(b1 + b2) x h]/2.

Area of Irregular Polygons

squarescovered

You can find the area of irregular polygons by decomposing the polygon into rectangles, triangles and other shapes.

Practice

Find the area of each shape.

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day 34.6This is 27, 24, 18, 30.

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(sources – GVLWikihow)