Quadrilaterals. 1. Find the length of the midsegment of the trapezoid.
EXAMPLE 1 Find the area of a trapezoid BASKETBALL The free-throw lane on an international basketball...
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EXAMPLE 1 Find the area of a trapezoid BASKETBALL The free-throw lane on an international basketball court is shaped like a trapezoid. Find the area of the free- throw lane.
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Transcript of EXAMPLE 1 Find the area of a trapezoid BASKETBALL The free-throw lane on an international basketball...
EXAMPLE 1 Find the area of a trapezoid
BASKETBALL
The free-throw lane on an international basketball court is shaped like a trapezoid. Find the area of the free-throw lane.
EXAMPLE 1 Find the area of a trapezoid
SOLUTION
The height of the trapezoid is 5.8 meters. The lengths of the bases are 3.6 meters and 6 meters.
A = h(b1 + b2)12
= (5.8)(3.6 + 6)12
= 27.84
Formula for area of a trapezoid
Substitute 5.8 for h, 3.6 for b1, and6 for b2.
Simplify.
The area of the free-throw lane is about 27.8 square meters.
ANSWER
EXAMPLE 2 Find the area of a rhombus
MUSIC
Rhombus PQRS represents one of the inlays on the guitar in the photo. Find the area of the inlay.
EXAMPLE 2 Find the area of a rhombus
STEP 1 Find the length of each diagonal. The diagonals of a rhombus bisect each other, so QN = NS and PN = NR.
QS = QN + NS = 9 + 9 = 18 mm
PR = PN + NR = 12 + 12 = 24 mm
STEP 2 Find the area of the rhombus. Let d1
represent QS and d2 represent PR.
SOLUTION
EXAMPLE 2
A = d1d212
= (18)(24)12
= 216
Formula for area of a rhombus
Substitute.
Simplify.
Find the area of a rhombus
The area of the inlay is 216 square millimeters.
ANSWER
GUIDED PRACTICE for Examples 1 and 2
Find the area of the figure
SOLUTION
The height of the trapezoid is 4ft. The lengths of the bases are 6ft and 8ft.
1.
GUIDED PRACTICE for Examples 1 and 2
= 28
= (4)(6 + 8)12
A = h(b1 + b2)12
Formula for area of a trapezoid
Substitute 4 for h, 6 for b1, and8 for b2.
Simplify.
The area of the figure is 28ft2.
ANSWER
GUIDED PRACTICE for Examples 1 and 2
2.
SOLUTION
= (6)(14)12
A = h(b1 b2)12
Formula for area of kite
Substitute.
= 42 Simplify.
area of kite is 42 in2.
ANSWER
GUIDED PRACTICE for Examples 1 and 2
SOLUTION
STEP 1
3.
Find the length of each diagonal. The diagonals of a rhombus bisect each other,
d1
d2
= 30 + 30 = 60 m
= 40 + 40 = 80 m
GUIDED PRACTICE for Examples 1and 2
STEP 2 Find the area of the rhombus.
Formula for area of a rhombusA = d1 d212
Substitute.= 60 8012
= 2400 Simplify.
The area of rhombus is 2400 m2.
ANSWER
