The question is below

Mathematics

1 answer:

Ad libitum [116K]2 years ago

7 0

Answer:

£59.25

Step-by-step explanation:

Hello!

To solve this problem, we must:

Solve for the length of the fence (aka height)
Find the area of the lawn (trapezoid)
Find the number of cans needed
Find the price of all the cans

Area of a trapezoid, and why the formula works:

A trapezoid is a quadrilateral with one set of parallel sides known as bases. The other two sides are known as the legs.

To find the area of a trapezoid, we use the formula:

$\frac{B_1 + B_2}{2}* h$

This works because if we used the formula, we would be duplicating the trapezoid to form a rectangle with a side length of B1 + B2, and a height of h. Since the trapezoid is half of that, we divide by 2.

Solve for height:

The height is unknown but can be found using the Pythagorean Theorem.

The difference between the bases is the length of the bottom leg of the right triangle, and 17 is the hypotenuse.

Difference = 20 - 12 = 8

Hypotenuse = 17

8² + fence² = 17²
64 + fence² = 289
225 = fence²
fence = 15

The height is 15

Solve for area:

Now we can solve for the area.

$A = \frac{B_1 + B_2}{2} * h$
$A = \frac{12 + 20}{2} * 15$
$A = \frac{32}{2} * 15$
$A = 16 * 15 = 240$

The area is 240

Cans:

The area of the lawn is 240 square meters. Each can cover 100 square meters.

240 ÷ 100 = 2.4

Since we can't use part of a can, we round up to three whole cans.

The price of 3 cans :

3 * 19.75
59.25

£59.25

The Pythagorean Theorem:

The Pythagorean theorem is a very common geometry formula used to find the length of the hypotenuse in a right triangle, given the lengths of the two other bases.

The formula is : $a^2 + b^2 = c^2$