In a quadrilateral abcd ab=40m bc=15 cd=28m ad=9m. find the area of the quadrilateral
Answers
Step-by-step explanation:
join ac then solve by Pythagoras theorem
then by find area
Step-by-step explanation:
AB =40 m
BC = 15 m
CD = 28 m
AD = 9 m
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Join BD
..
(AB)² + (AD)² = (BD)²
(40)² + (9)² = (BD)²
1600 + 81 = (BD)²
1681 = (BD)²
BD = 41
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Area of triangle ABD
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a = 40 m
b = 9 m
c = 41 m
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semi perimeter = a + b + c
—————
2
= 40 + 9 + 41
—————–—
2
= 90 ÷ 2
= 45m
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Area = use heron's formula
= under root [ s ( s - a ) ( s - b ) ( s - c ) ]
= under root [ 45 ( 45 - 40 ) ( 45 - 9 ) ( 45 - 41 )]
= under root [ 45 × 5 × 36 × 4]
= 6 × 2 under root [ 9 × 5 × 5 ]
= 12 × 5 under root [ 9 ]
= 60 ×3
= 120 m² ............... ( 1 )
..
..
Area of triangle BDC
a = 15 m
b = 28 m
c = 41 m
..
semi perimeter = a + b + c
—————
2
15 + 28 + 41
= —————
2
= 84
——
2
= 42 m
..
..
Area = use heron's formula
= under root [ s ( s - a ) ( s - b ) ( s - c ) ]
= under root [ 42 ( 42 - 15 ) ( 42 - 28 ) ( 42 - 41 )
= under root ( 42 × 27 × 14 × 1 )
= under root (2× 3 × 7 × 3 × 3 × 3 × 7 × 2)
= 2 × 3 × 7 × 3
= 126 m² ......... ( 2 )
.
..
...
□ABCD = triangle ABD + triangle BDC
=120 m² + 126 m² = 246 m²
..
..
area of quadrilateral ABCD = 246 m²
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