Question

See attached the question is in an image attached

Answer 1

30.51 units^2

Explanation:

Well to find the area of a triangle without height we use the following formula,

`A = √(S(S-a)(S-b)(S-c))`

To find S we use the following formula,

`S = (1)/(2) (a+b+c)`

So a b and c are the sides of a triangle, we'll start with the left triangle.

S = 1/2(7 + 5.22 + 7.4)

S = 1/2(19.62)

S = 9.81

Now we can plug in 9.81 for S,

`A = √(9.81(9.81-a)(9.81-b)(9.81-c))`

`A = √(9.81(9.81-7)(9.81-5.22)(9.81-7.4))`

`A = √(9.81(2.81)(4.59)(2.41))`

`A = √(9.81(31.083939))`

`A = √(304.93344159)`

`A = 17.46234353086664`

But we can just simplify that to the nearest hundredth place which is,

17.46.

Now for the next triangle,

`S = (1)/(2) (6.36 + 6.85 + 7.4)`

`S = (1)/(2) (20.61)`

`S = 10.305`

Plug in 10.305 for S,

`A = √(10.305(10.305-6.36)(10.305-6.85)(10.305-7.4))`

`A = √(10.305(3.945)(3.455)(2.905))`

`A = √(10.305(16.534975))`

`A = √(170.392917375)`

A = 13.053463807549

We can round it to the nearest hundredth,

A = 13.05

So we just add 17.46 + 13.05

= 30.51 units^2

Thus,

the area of the figure is 30.51 units^2.

Hope this helps :)

Answer 2

37.62202 sq units

First, calculate the areas of the separate triangles:

ABD = 20.19968 sq units

ACD = 17.46234 sq units

then add them to get 37.62202 sq units