First, let's establish what we know about the two triangles--without doing any calculations. The height of the green triangle is 2, and the width of its base is 5. The height of the red triangle is 3, and the width of its base is 8. Just to verify the statement on the site, you can easily count the squares to ensure this.
Okay, now let's take a look at the first large triangle. The green triangle is on top, and its base forms the top of the rectangle (the two shapes inside are irrelevant for right now). The red triangle is to the left, and its right edge forms the left side of the rectangle. This yields a rectangle of length 5 and height 3, and with an area of (5 * 3) = 15.
The second triangle switches the red triangle and the green triangle. This means the bottom of the red triangle forms the top of the rectangle (still ignoring the two shapes inside), and the right side of the green triangle forms the left side of the rectangle. This yields a rectangle of length 8 and height 2, and with an area of (8 * 2) = 16.
Okay, well now this says that there is one extra space, but why is there a hole? This is simply because the two shapes, while forming a rectangle of area 15 in the first triangle, still have a combined area of 15 in the second. Why? The way the shapes were separated allows them to be combined so as to look like a 8 x 2 rectangle, but, since you can't create extra area that didn't exist before, the shapes naturally have a "hole."
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whats the answer?
Answer:
First, let's establish what we know about the two triangles--without doing any calculations. The height of the green triangle is 2, and the width of its base is 5. The height of the red triangle is 3, and the width of its base is 8. Just to verify the statement on the site, you can easily count the squares to ensure this.
Okay, now let's take a look at the first large triangle. The green triangle is on top, and its base forms the top of the rectangle (the two shapes inside are irrelevant for right now). The red triangle is to the left, and its right edge forms the left side of the rectangle. This yields a rectangle of length 5 and height 3, and with an area of (5 * 3) = 15.
The second triangle switches the red triangle and the green triangle. This means the bottom of the red triangle forms the top of the rectangle (still ignoring the two shapes inside), and the right side of the green triangle forms the left side of the rectangle. This yields a rectangle of length 8 and height 2, and with an area of (8 * 2) = 16.
Okay, well now this says that there is one extra space, but why is there a hole? This is simply because the two shapes, while forming a rectangle of area 15 in the first triangle, still have a combined area of 15 in the second. Why? The way the shapes were separated allows them to be combined so as to look like a 8 x 2 rectangle, but, since you can't create extra area that didn't exist before, the shapes naturally have a "hole."
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