if triangle ABC is a right triangle and BC is a semicircle, find the total area of the figure below. what is the diameter of the semi-circle

Question

if triangle ABC is a right triangle and BC is a semicircle, find the total area of the figure below. what is the diameter of the semi-circle? _____ units.
Area=____ units squared (rounded to the nearest hundredth. )
side AB is 3 units long.
Side AC is 4 units long.

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Arianna 4 weeks 2021-09-25T22:55:11+00:00 1 Answer 0

Answers ( )

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    2021-09-25T22:56:21+00:00

    Area of the semi-circle = 9.8125 square units

    Solution:

    Given ABC is a right triangle.

    BC is a semi-circle.

    ∠BAC = 90°.

    AB = 3 units and AC = 4 units.

    BC is the hypotenuse of the right triangle ABC.

    Using Pythagoras theorem,

    In right triangle, square of the hypotenuse is equal to the sum of the squares of the other two sides.

    BC^2=AB^2+AC^2

    BC^2=3^2+4^2

    BC^2=25

    Take square root on both sides.

    BC = 5 units

    The diameter of the semi-circle is 5 units.

    Radius = 5 ÷ 2 = 2.5 units

    Area of the semi-circle = \frac{1}{2}\pi r^2

                                          =\frac{1}{2}\times 3.14\times 2.5^2

                                          = 9.8125 square units

    Area of the semi-circle = 9.8125 square units

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45:7+7-4:2-5:5*4+35:2 =? ( )