Answer (bolded and underlined):
The area of Charlen's rhombus is 1/9 of the area of Jerry's rhombus
The base of Charlene's rhombus is 5 inches and the height is 3 inches, giving it an area of 15 square inches
Explanation:
One of the formulas we can use for area of a rhombus is given by,
A = bh, where
- A is the area in square units,
- b is the base,
- and h is the height.
Area of Jerry's Rhombus: First, we can calculate the area of Jerry's rhombus by plugging in 15 for b and 9 for h in the area formula and simplifying:
A = 15 * 9
A = 135 in^2
Thus, the area of Jerry's rhombus is 135 in^2.
Area of Charlen's Rhombus: Before we're able to find the area of Charlene's rhombus, we'll need to find the base and height:
Base of Charlene's Rhombus: Since we're told that the base of Charlene's rhombus is 1/3 the base of Jerry's, we can find the base by multiplying 1/3 by 15 (base of Jerry's rhombus):
b = 1/3 * 15
b = 15/3
b = 5 in
Height of Charlen's Rhombus: Since we're told that the height of Charlene's rhombus is 1/3 the height of Jerry's, we can find the height by multiplying 1/3 by 9 (height of Jerry's rhombus):
h = 1/3 * 9
h = 9/3
h =3 in.
Now that we know the base and height of Charlen's rhombus, we can find the area of Charlen's rhombus by plugging in 5 for b and 3 for h in the area formula and simplifying:
A = 5 * 3
A = 15 in^2
Thus, the area of Charlene's rhombus is 15 in^2
Comparing the areas of Charlene and Jerry's rhombi:
- We see that the area of Charlen's rhombus is 15 and the area of Jerry's rhombus is 135.
- If we divide the two values, we get 135 / 15 = 9.
- Thus, the area of Charlen's rhombus is 1/9 the area of Jerry's rhombus, which you can see by multiplying 1/9 by 135:
1/9 * 135 = 15