Answer:
44.47 cm² (nearest hundredth)
Step-by-step explanation:
Area of ΔABC = 1/2 x base x height
⇒ 21 = 1/2 x 7 x BC
⇒ BC = 6 cm
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
⇒ AB² + BC² = AC²
⇒ 7² + 6² = AC²
⇒ AC² = 85
⇒ AC = √85 cm
Cosine rule to find length AD:
c² = a² + b² - 2 ab cosC
⇒ DC² = AD² + AC² - 2(AD)(AC)cos(DAC)
⇒ 9.2² = AD² + (√85)² - 2(AD)(√85)cos 73°
⇒ AD² - 5.39106...AD + 0.36 = 0
⇒ AD = 5.323442445, 0.06762541414
⇒ AD = 5.323442445
Area of a triangle ADC: (1/2)absinC
(where a and b are adjacent sides and C is the angle between them)
⇒ area = (1/2) × AC × AD × sin(DAC)
⇒ area = (1/2) × √85 × 5.323442445 × sin(73°)
⇒ area =23.4675821... cm²
Area of quadrilateral = area of ΔABC + area of ΔADC
= 21 + 23.4675821...
= 44.47 cm² (nearest hundredth)
Answer:
Below
Step-by-step explanation:
All figures are squares. The area of a square is the side times itself
Let A be the area of the big square and A' the area of the small one in all the 5 exercices
51)
● (a) = A - A'
A = c^2 and A' = d^2
● (a) = c^2 - d^2
We can express this expression as a product.
● (b) = (c-d) (c+d)
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52)
● (a) = A-A'
A = (2x)^2 = 4x^2 and A'= y^2
● (a) = 4x^2 - y^2
● (b) = (2x-y) ( 2x+y)
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53)
● (a) = A-A'
A = x^2 and A' = y^2
● (a) = x^2-y^2
● (b) = (x+y) (x-y)
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54)
● (a) = A-A'
A = (5a)^2 = 25a^2 and A' =(2b)^2= 4b^2
● (a) = 25a^2 - 4b^2
● (a) = (5a-2b) (5a+2b)
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55)
● (a) = A - 4A'
A = (3x)^2 = 9x^2 and A'= (2y)^2 = 4y^2
● (a) = 9x^2 - 4 × 4y^2
● (a) = 9x^2 - 16y^2
● (a) = (3x - 4y) (3x + 4y)
There will be 8 ways to not pick yellow because there are 4 yellow and 3 green and blue and 2 red
Answer:
Hi there!
The correct answer to this question is: 200.96 ft²
Step-by-step explanation:
The equation for the area of circle is A = πr² you know the radius so just plug in the values and you get A = (3.14)(8)² and you get 200.96
