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Use the information on the diagonal to find: a. the length ACb. the length ABc. the perimeter of quadrilateral ABCDd. the area of quadrilateral ABCD

Use the information on the diagonal to find: a. the length ACb. the length ABc. the-example-1
User Tim Fuqua
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2 Answers

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c, explaination: edge 22'
User Haphil
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A) To find the length AC, we must use the trigonometric ratio


\cos \text{ 31 =}(adjacent)/(hypothenuse)

adjacent = 5cm

hypothenuse = AC


\begin{gathered} \cos 31\text{ = }(5)/(AC) \\ AC\text{ = }(5)/(\cos 31) \\ AC\text{ =}5.8332\operatorname{cm} \end{gathered}

B) To find the length AB, we will use the value of AC just obtained to get it

since triangle ABC is a right-angled triangle, we will use Pythagoras theorem

so that

|AC|^2 = |AB|^2 +|BC|^2

AC = 5.8332cm

BC = 4cm

|AB|^2 = |AC|^2 - |BC|^2


\begin{gathered} AB\text{ = }\sqrt[]{5.8332^2-4^2} \\ AB\text{ = }\sqrt[]{18.0262224} \\ AB\text{ = 4.245729883cm} \end{gathered}

C) The perimeter of the quadrilateral can be found by adding the length of all the sides around its edges.

Perimeter = AD +CD + BC + AB

We do not have CD and we must find CD


\begin{gathered} CD\text{ = }\sqrt[]^2- \\ CD\text{ =}\sqrt[]{5.8332^2-5^2} \\ CD\text{ =}\sqrt[]{9.02622224} \\ CD\text{ = 3.004366195cm} \end{gathered}

Perimeter of ABCD = 5 + 3.004366195 + 4 +4.245729883 = 16.25009708cm

D) To find the area of the quadrilateral we must find the area of triangle ADC and triangle ABC.

Area of triangle ADC = 1/2 x base x height= 1/2 x 3.004366195 x 5 = 7.510915488 square centimeter

Area of triangle ABC = 1/2 X base x height = 1/2 x 4 x 4.245729883 =8.491459766 square centimeter

Area of quadrilateral ABCD = 7.510915488 + 8.491459766 = 16.00237525 square centimeter

User Rini
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