Answer:
90 units^2
Step-by-step explanation:
Let's first label this rhombus, attached in the image below- (sorry if it's a little abstruse).
Now let's find the area of all the triangles inside the rhombus so we can add them all up in the end to get the total area of the rhombus.
To find the area of a triangle, we just need the base and height.
In this case for the four right triangles, their base lengths are 3 while their heights are 15, as shown in the picture with the pink highlights.
We can find their areas in two ways, one more convenient.
We would find the area of the four individual right triangles formed by the diagonals and add them up to get the area of the rhombus. However- there is a shortcut.
Notice how you can combine both pairs of right triangles on opposite angles(left and right) of the rhombus to form two complete triangles.
If we do this, we would have to change the base length of the triangles as their base got bigger when we used the two pairs of right triangles to form these triangles.
So we can revert back to the original length of the diagonal that cuts it vertically and say that the base for both triangles is 6 units long. The heights would remain the same, 15 units.
Now let's solve for the area of these two triangles using the formula for the area of a triangle which is:
A = 1/2BH, b represents base and h represents height.
Given for both triangles:
Height = 15
Base = 6
Plug this into the formula and solve for one triangle, then double its area to get the sum of both their areas combined.
A = 1/2BH
Substitute:
A = 1/2(6)(15)
A = 3(15)
A = 45
Double its area as previously mentioned to get the total area of the rhombus (aka the two triangles' areas combined together):
2(45)
= 90.
The area of this rhombus is 90 units.
