Help me solve this (pls show working)

Mathematics

1 answer:

maksim [4K]3 years ago

6 0

Answer:

The area of the polygon is 92.75 cm^2

Step-by-step explanation:

To find the area of the polygon, we simply add up the areas of the constituent triangles

At any point in time;

Area of a triangle = 1/2 * base * height

So we proceed as follows;

(1/2 * 12 * 4.5) + (1/2 * 12 * 5)

= 27 + 30 = 57 cm^2

There is a last triangle with 12 cm and 5 cm as the sides and we need the length of the hypotenuse

The length of the hypotenuse for that triangle will be 13 cm. This is because 5,12 and 13 are Pythagorean triple and they form the sides of a right-angled triangle

So for the last triangle, the area will be;

1/2 * 13 * 5.5 = 35.75 cm^2

So the total area is;

35.75 + 57 = 92.75 cm^2

You might be interested in

A system for tracking ships indicated that a ship lies on a hyperbolic path described by 5x2 - y2 = 20. the process is repeated

zysi [14]

Answer:
The ship is located at (3,5)

Explanation:
In the first test, the equation of the position was:
5x² - y² = 20 ...........> equation I
In the second test, the equation of the position was:
y² - 2x² = 7 ..............> equation II
This equation can be rewritten as:
y² = 2x² + 7 ............> equation III

Since the ship did not move in the duration between the two tests, therefore, the position of the ship is the same in the two tests which means that:
equation I = equation II

To get the position of the ship, we will simply need to solve equation I and equation II simultaneously and get their solution.

Substitute with equation III in equation I to solve for x as follows:
5x²-y² = 20
5x² - (2x²+7) = 20
5x² - 2y² - 7 = 20
3x² = 27
x² = 9
x = <span>± </span>√9

We are given that the ship lies in the first quadrant. This means that both its x and y coordinates are positive. This means that:
x = √9 = 3

Substitute with x in equation III to get y as follows:
y² = 2x² + 7
y² = 2(3)² + 7
y = 18 + 7
y = 25
y = +√25
y = 5

Based on the above, the position of the ship is (3,5).

Hope this helps :)

8 0

3 years ago

The prime factorizations of 54 and 72 are shown below.

Karo-lina-s [1.5K]

Your answer is 2’3’3!! (2*3*3 = 18)

hopefully this helps, good luck bud! :)