I need help with find the area of the other shapes. Like you can give me an example of the width and lenth like this (8:7) and I
'll put a pic of what I've got so far and I need you to do what I did please.I really need help.
You must include the following items: • At least 10 shapes in which you can calculate the area (label the dimensions for each shape in feet 1 cm=3.25feet) o 2 rectangles o 1 rhombus o 3 triangles (1 must include a fractional base) o 2 trapezoids (1 base must be a decimal) o 1 pentagon o 1 irregular polygon in which you’ll have to decompose into smaller shapes. And if my pic ain't clear enough sorry.
You must include the following items: • At least 10 shapes in which you can calculate the area (label the dimensions for each shape in feet 1 cm=3.25feet) o 2 rectangles o 1 rhombus o 3 triangles (1 must include a fractional base) o 2 trapezoids (1 base must be a decimal) o 1 pentagon o 1 irregular polygon in which you’ll have to decompose into smaller shapes. And if my pic ain't clear enough sorry.
2 answers:
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<h3>Answer: As a fraction, HC is 21/4 units long</h3><h3>In decimal form, HC is 5.25 units long.</h3>
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Work Shown:
Let x = HC and y = BH
AH = 12-x since AH = 12-HC and x = HC
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See the attached drawing below. The altitude BH forms three similar triangles which makes the proportion below possible
HC/BH = BH/AH
x/y = y/(12-x) ... substitution
x(12-x) = y^2 ... cross multiply
y^2 = -x^2+12x
note how I isolated y^2 instead of y. We will use this equation later.
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Focus on triangle AHB. Use the pythagorean theorem
(BH)^2 + (AH)^2 = (AB)^2
(y)^2 + (12-x)^2 = (9)^2
y^2 + 144-24x+x^2 = 81
-x^2+12x + 144-24x+x^2 = 81 ... replace y^2 with -x^2+12x
-x^2+12x + 144-24x+x^2-81 = 0
-12x + 63 = 0
-12x = -63
x = -63/(-12)
x = 5.25 <<-- answer in decimal form
x = 5 + 0.25
x = 5 + 1/4
x = 20/4 + 1/4
x = 21/4 <<-- answer as a fraction