a We are given a tangram that is a 4-inch square, and we are asked to evaluate the perimeter and area of the purple triangle. Let's take a look at the given diagram. Notice that this tangram consists of 16 one-inch squares.
To evaluate the perimeter we need to add all side lengths of this triangle. Recall that in a square the length of the diagonal is 2 times the side length. This means that the diagonal of each 1-inch square is 2.
As we have all the side lengths of this triangle, we can evaluate its perimeter. We will round our result to the nearest tenth using a calculator.
P=4+2+2+2+2≈9.7
The perimeter of the purple triangle is approximately 9.7 inches. Now, let's recall that the area of a triangle is the half of the product of its base and height. Looking at our diagram we can see that the base of the purple triangle is 4 and the corresponding height is 2.
Knowing the base and the height of this triangle, we can evaluate its area.
A=21(4)(2)=4
The area of the purple triangle is 4 square inches.
b In this part we are asked to evaluate the perimeter and area of the blue parallelogram. Let's take a look at the given diagram. Notice that this tangram consists of 16 one-inch squares.
To evaluate the perimeter we need to add all side lengths of this parallelogram. Recall that in a square the length of diagonal is 2 times the side length. This means that the diagonal of each 1-inch square is 2.
As we have all side lengths of this parallelogram, we can evaluate its perimeter. We will round our result to the nearest tenth using a calculator.
P=2+2+2+2≈6.8
The perimeter of the blue parallelogram is approximately 6.8 inches. Now, let's recall that the area of a parallelogram is the product of its base and height. Looking at our diagram we can see that the base of the parallelogram is 2 and the height is 1.
Knowing the base and the height of this parallelogram we can evaluate its area.
A=2⋅1=2
The area of the blue parallelogram is 2 square inches.
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