Question

HELP PLEASE!!! I need your guys help on this question.

Answer 1

The first (left) trapezoid's area is
`10√(55)`m or ≈ 74.2m²

The second (right) trapezoid's area is
`54 +18√(3)` or ≈ 85.2 in²

Explanation:

First trapezoid (left):

Because the first trapezoid is a normal trapezoid, we can use the equation
`A = (a+ b)/(2) * h` Where a is equal to one base length and b is equal to the other base length and h is the height of the trapezoid.

a = 7

b = 13

h =
`√(55)` (
`3^(2)+h^(2) = 8^(2)`)

Plug into the equation:

`A = (7+13)/(2) *√(55)`

A =
`10√(55)` or ≈74.2m²

Second trapezoid (right):

Not a normal trapezoid (split into a triangle and a square)

Let's solve for the triangle first:

using
`sin(30) = (x)/(12)` to find the right-hand side of the triangle we get x = 6

because this is a 30 60 triangle, the last side has to be
`6√(3)`

Now we can calculate the area of the figure:

Triangle is
`(1)/(2) * 6 * 6√(3) = 18√(3)`

Rectangle is 6 * 9 = 54

Area =
`54 +18√(3)` or ≈ 85.2 in²

Answer 2

Area of a trapezium = 1/2(a+b)×h

where a and b are parallel sides of the trapezium

h is the height

First question

We must first find the height of the trapezium using Pythagoras theorem

That's

h² = 8² -3²

h =√ 64 - 9

h = √ 55m

a = 7m

b = 10+3 = 13m

Area of the trapezoid = 1/2(7+13)×√55

= 1/2×20×√55

= 74.16

= 74m² to the nearest tenth

Second question

We use sine to find the height

sin30° = h/12

h = 12 sin 30°

h = 6 in

Let the other half of the parallel side be x

To find the other half of the parallel side we use Pythagoras theorem

That's

x² = 12²- 6²

x = √144-36

x = √108

x = 6√3 in

So for this trapezoid

a = 9 in

b = (9 + 6√3) in

h = 6 in

Area of the trapezoid = 1/2(9 + 9+6√3) × 6

= 1/2(18+6√3)×6

= 85.176 in²

= 85 in² to the nearest tenth

Hope this helps you