Find the area of the shaded figure, rounded to two decimals. (Assume x = 1 and y = 4.)

Question

Answer 1

I am assuming that this is a square pyramid and the part that you cannot see is also shaded. (if not, just take half of the answer)

Take one triangle and draw its height (h).

The height bisects the base of 1 into two pieces, each 1/2.

Use the Pythagorean Theorem to find h.

4^2=(1/2)^2+h^2

16=1/4 + h^2

h^2=16-(1/4)

h^2=15 3/4

h^2=63/4

take the square root of both sides

h=√63/2

Now find the area of this triangle.

A=(1/2)bh

A=(1/2)(1)(√63/2)

A=√63/4 square units

There are 4 of these triangles, all congruent to each other.

4*√63/4=√63 square units for the areas of the four triangles

The area of the square base is 1*1=1 square unit.

The area of the figure is (√63+1) square units

If you want half only, the answer is (√63+1)/2 square units

√63=7.937

7.937+1=8.94 square units rounded

or, 8.94/2=4.47 square units