Which equation can be used to calculate the area of the shaded triangle in the figure below?

A rectangle with length of 12 feet and width 4 feet. A diagonal cuts the rectangle into two halves. One of the triangular halves is shaded.

2(12 + 4) = 32
fraction 1 over 2(12 + 4) = 8
2(12 × 4) = 96
fraction 1 over 2(12 × 4) = 24

Option (2) is correct.

Area of shaded region is \frac{1}{2} \times(12 \times 4)=24 \text{square feet}

Step-by-step explanation:

As per the given information, figure below shows a rectangle with a width of 4 ft and a length of 12 ft. There is a diagonal line through the rectangle, and the bottom half is shaded in grey.

Area of rectangle = Length × width

Area of given rectangle = 12 × 4 = 48 ft²

Since we have to find the area of shaded region which is half of the area of whole rectangle as diagonal divide the rectangle into two equal triangles.

Thus, area of shaded region is half the area of rectangle.

AREA OF SHADED REGION =

                                           ft²

thus, area of shaded region is

Option (2) is correct.

Hope it helps!

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

a: 1/6, j: 1/4

step-by-step explanation: you are welcome