10-1 Areas of Parallelograms and Triangles

Quick Review

You can find the area of a rectangle, a parallelogram, or a triangle if you know the base b and the height h.

The area of a rectangle or parallelogram is A = b h . eh equals b h .

The area of a triangle is A = 1 2 b h . eh equals . 1 half , b h .

Example

What is area of the parallelogram?

A = b h Use the area formula .   = ( 12 ) ( 8 ) = 96 Substitute and simplify . table with 2 rows and 3 columns , row1 column 1 , eh , column 2 equals b h , column 3 cap usetheareaformula . . , row2 column 1 , , column 2 equals , open 12 close . open 8 close , equals 96 , column 3 cap substituteandsimplify . . , end table

The area of the parallelogram is 96   cm 2 . 96 , cm squared , .

Exercises

Find the area of each figure.

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9. A right triangle has legs measuring 5 ft and 12 ft, and hypotenuse measuring 13 ft. What is its area?

10-2 Areas of Trapezoids, Rhombuses, and Kites

Quick Review

The height of a trapezoid h is the perpendicular distance between the bases, b 1 b sub 1  and b 2 . b sub 2 , .

The area of a trapezoid is A = 1 2 h ( b 1 + b 2 ) . eh equals . 1 half , h . open , b sub 1 , plus . b sub 2 , close .

The area of a rhombus or a kite is A = 1 2 d 1 d 2 , eh equals , 1 half , d sub 1 . d sub 2 , comma  where d 1 d sub 1  and d 2 d sub 2  are the lengths of its diagonals.

Example

What is the area of the trapezoid?

A = 1 2 h ( b 1 + b 2 ) Use the area formula .   = 1 2 ( 8 ) ( 7 + 3 ) Substitute .   = 40 Simplify . table with 3 rows and 3 columns , row1 column 1 , eh , column 2 equals , 1 half , h open , b sub 1 , plus , b sub 2 , close , column 3 cap usetheareaformula . . , row2 column 1 , , column 2 equals , 1 half . open 8 close . open , 7 plus 3 , close , column 3 cap substitute . . , row3 column 1 , , column 2 equals 40 , column 3 cap simplify , . , end table

The area of the trapezoid is 40   cm 2 . 40 , cm squared , .

Exercises

Find the area of each figure. If necessary, leave your answer in simplest radical form.

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14. A trapezoid has a height of 6 m. The length of one base is three times the length of the other base. The sum of the base lengths is 18 m. What is the area of the trapezoid?

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