Question

Which figures have equal area? Choose all that are correct.

Answer 1

What does it mean to have something be equal (Equivalent)?

Equivalence means to be same, whether it be value, temperature, size, etc.

Let's take a look at shape 1.

Shape 1 has a base of 3, and a height of 4, but there is a gap with a width of 1 and a height of 2. So, we can use this equation to figure out the area:

• (3 × 4) - (1 × 2) = 10

So, shape 1 has an area of 10 units.

Let's look at shape 2.

Shape 2 has a base of 2, and a height of 4, but there is also a gap, with a width of 1 and a height of 3. So, we can use this equation to figure out the area:

• (2 × 4) - (1 × 3) = 5

So, shape 2 has an area of 5 units.

Let's look at shape 3.

Shape 3 consists of 4 right triangles, put together to form an arrowhead. The shape has a base of 4, and a height of 2. So, we can use this equation to figure out the area:

• (4 × 2) ÷ 2 = 4

So, shape 3 has an area of 4 units.

Let's look at shape 4.

Shape 4 consists of 4 right triangles, put together to form a diamond. The shape has a base of 4, and a height of 2. So, we can use this equation to figure out the area:

• (4 × 2) ÷ 2 = 4

So, shape 4 has an area of 4 units.

Looking to the final shape (5), we can see it consists of a long rectangle and 2 right triangles. Instead of calculating the base and height of the entire shape, we can break it into pieces, making a rectangle that has a base of 3, and a height of 1. Then we are left a shape that has a base of 2, and a height of 3. So, we can use this equation to figure out the area:

• (3 × 1) + ([2 × 3] ÷ 2) = 6

So, shape 5 has an area of 6 units.

Let's compare the area of all of the shapes.

1. Has an area of 10 square units.
2. Has an area of 5 square units.
3. Has an area of 4 square units.
4. Has an area of 4 square units.
5. Has an area of 6 square units.

Therefore, the two figures that have equal areas are shapes 3 and 4.