All categories

2 years ago

The shaded area and the diameter

Mathematics

2 answers:

masha68 [24]2 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]2 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

You might be interested in

For the graphed exponential equation, calculate the average rate of change from x = −3 to x = 0.

iragen [17]

Answer:

$-\frac{7}{3}$

Step-by-step explanation:

To solve this, we are using the average rate of change formula:

$m=\frac{f(b)-f(a)}{b-a}$

where

$m$ is the average rate of change

$a$ is the first point

$b$ is the second point

$f(a)$ is the function evaluated at the first point

$f(b)$ is the function evaluated at the second point

We want to know the average rate of change of the function $f(x)=0.5^x-6$ form x = -3 to x = 0, so our first point is -3 and our second point is 0. In other words, $a=-3$ and $b=0$ .

Replacing values

$m=\frac{f(b)-f(a)}{b-a}$

$m=\frac{0.5^0-6-(0.5^{-3}-6)}{0-(-3)}$

$m=\frac{1-6-(8-6)}{3}$

$m=\frac{-5-(2)}{3}$

$m=\frac{-5-2}{3}$

$m=\frac{-7}{3}$

$m=-\frac{7}{3}$

We can conclude that the average rate of change of the exponential equation form x = -3 to x = 0 is $-\frac{7}{3}$

4 0

3 years ago

Triangle ABC is an obtuse triangle with the obtuse angle at vertex B. Angle A must be

kvv77 [185]

Answer:

Angle A must be acute.

Explanation:

Both angle A and C must be acute. The sum of the angles in a triangle is 180°.

An obtuse angle is more than 90°, so the sum of the remaining 2 angles has to be less than 90°.

Note that it is impossible to have:

2 right angles in a triangle, because 90°+90°=180° and the third angle still needs to be added.1 obtuse and 1 right angle in a triangle, their sum is more than 180°2 obtuse angles in a triangle, their sum is more than 180°

It is possible to have an obtuse-angled isosceles triangle, but the vertex angle must be obtuse and the equal base angles will be acute.

8 0

3 years ago

Câu 1. Cho ánh xạ f : R

9966 [12]

what is your clear question? it lacks some details

4 0

3 years ago

Please Help Me!!!!!! I have a big test tomorrow!!!!!!!! I will give 30 points!!!!!!!!! The expression represents the number of m

il63 [147K]

Answer:

For this expression I guessed I would use subtraction because when you subtract Kimiko's miles to Celeste's miles you could see how much faster Kimiko was than Celeste.

Step-by-step explanation:

4 0

2 years ago

Two numbers are in the ratio 3:4 when 4 is added to each term their ratio becomes 10:13. Find the numbers.

Alex17521 [72]

So there’s 2 steps to this. First we subtract what was added on both sides. 10-4 : 13-4 and we get 6:9. This ratio is true, but is not in simplest form, since both numbers are divisible by 3. So after dividing both sides by 3, the answer in simplest form will be 2:3. The correct answer is 2:3

7 0

3 years ago