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3 years ago

The shaded area and the diameter

Mathematics

2 answers:

masha68 [24]3 years ago

7 0

Answer:

15.25 cm²

Step-by-step explanation:

The diameter is the hypotenuse of the triangle:

d = √8²+6² = √100 = 10 cm

Area of the semicircle:

A = 1/2πr² = 1/2(3.14)(10/2)² = 39.25 cm²

Area of the triangle:

A = 1/2bh = 1/2(6)(8) = 24 cm²

Shaded area:

39.25 - 24 = 15.25 cm²

Mariana [72]3 years ago

6 0

Answer:

Area of shaded region is 15.25 m

Step-by-step explanation:

Step 1 :- Finding the Diameter

As we know that length of the hypotenuse of triangle is the diameter of circle

To find length of hypotenuse using Pythagoras theorem

(a)²+(b)²= (c)²

Where, a and b is the legs and c is the length of hypotenuse of triangle.

( 8m ) ² + ( 6m ) ² = ( c ) ²

64m² + 36m² = c ²

Combine like terms

100 m² = c ²

Taking square root of each side

√100 m ² = √c²

10 m = c

Hypotenuse is the diameter of circle which is 10m.

Diameter = 10 m

Radius , r = 10 / 2 = 5 m

Step 2:- Finding the area of semi- circle

Area of semi-circle = 1 / 2 π r²

substitute the values

Area of semi-circle = 1 / 2 × π × ( 5 m )²

Evaluate the exponent

Area of semi-circle = 1 / 2 × π × 25 m²

Using value of π = 3.14

Area of semi-circle = 1 / 2 × 3.14 × 25 m²

Multiply , we get

Area of semi-circle = 39.25 m²

Step 3 :- Finding the area of triangle

Area of triangle = 1/2 × base × height

Where , base = 6 m and height = 8 m

substitute the values

Area of triangle = 1/2 × 6m × 8m

multiply,

Area of triangle = 1/ 2× 48 m²

Divide

Area of triangle = 48 m² / 2

Area of triangle = 24 m ²

Step 4 :- Area of shaded region is given by

= Area of semicircle - area of triangle

= 39.25 m² - 24 m² = 15.25 m

Hence , Area of shaded region is 15.25 m

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