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3 years ago

Find the Area of Triangles when lengths of the sides are given below.

Mathematics

2 answers:

ss7ja [257]3 years ago

6 0

Step-by-step explanation:

you should detect which one in the hypothenus!!

Naily [24]3 years ago

5 0

Answer:

84 cm² and 272 cm² (3 sf)

Step-by-step explanation:

Use Heron's formula.

Area = $\sqrt{p(p-a)(p-b)(p-c)}$

where a, b, and c are the lengths of the sides of the triangle

and $p=\frac{a+b+c}{2}$

(i) $p=\frac{13+14+15}{2}=21$

Area = $\sqrt{21(21-13)(21-14)(21-15)} = 84$ cm²

(ii) $p=\frac{103+115+13}{2}=115.5$

Area = $\sqrt{115.5(115.5-103)(115.5-115)(115.5-13)} = \frac{ \sqrt{1183875}}{4} =272$ cm² (3 sf)

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A cylinder has radius r and height h. A. How many times greater is the surface area of a cylinder when both dimensions are multi

Ierofanga [76]

Answer: A. Factor 2 => 4x greater

Factor 3 => 9x greater

Factor 5 => 25x greater

Step-by-step explanation: A. A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:

A = 2.π.r.h

A cylinder of radius r and height h has area:

$A_{1}$ = 2πrh

If multiply both dimensions by a factor of 2:

$A_{2}$ = 2.π.2r.2h

$A_{2}$ = 8πrh

Comparing $A_{1}$ to $A_{2}$ :

$\frac{A_{2}}{A_{1}}$ = $\frac{8.\pi.rh}{2.\pi.rh}$ = 4

Doubling radius and height creates a surface area of a cylinder 4 times greater.

By factor 3:

$A_{3} = 2.\pi.3r.3h$

$A_{3} = 18.\pi.r.h$

Comparing areas:

$\frac{A_{3}}{A_{1}}$ = $\frac{18.\pi.r.h}{2.\pi.r.h}$ = 9

Multiplying by 3, gives an area 9 times bigger.

By factor 5:

$A_{5} = 2.\pi.5r.5h$

$A_{5} = 50.\pi.r.h$

Comparing:

$\frac{A_{5}}{A_{1}}$ = $\frac{50.\pi.r.h}{2.\pi.r.h}$ = 25

The new area is 25 times greater.

B. By analysing how many times greater and the factor that the dimensions are multiplied, you can notice the increase in area is factor². For example, when multiplied by a factor of 2, the new area is 4 times greater.

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