Question

What is the area of the figure below?

A. 45 in.²
B. 90 in.²
C. 135 in.²
D. 180 in.²

Answer 1

each of the 4 inside triangles are right-angled and of the same size.

area of 1 inside triangle = base x height / 2 = 7.5 x 6 /2 = 22.5

total area = 4 x inside triangle = 4 x 22.5 = 90 in^2

so ans is B

Answer 2

Answer:B.  $90\ in^2$

Step-by-step explanation:

In the given picture we have a parallelogram such that there are 4 triangles formed by intersecting diagonals.

We know that the area of triangle is given by :-

$A=\frac{1}{2}\times base\times height\\\\\Rightarrow\ A=\frac{1}{2}\times6\times7.5=22.5\ in.^2$

Thus, area of one triangle inside parallelogram = $22.5\ in.^2$

Since diagonals of a parallelogram bisects each other.

Therefore, all the triangles inside the parallelogram are congruent to each other by SSS postulate.

Then the area of parallelogram =$4\times\text{area of one triangle inside parallelogram}[\tex]

[tex]4\times22.5=90\ in^2$