An image of object obtained by attaching&nbsp; triangle with one side length z is attached to a&nbsp; rectangle&nbsp; with base&nbsp; C&nbsp; and width w . The other two sides of triangle are X,Y and height H.
Note: Figure is not drawn to scale.

If Y = 14 inches, Z = 19 inches, H = 6 inches, and W = 4 inches, what is the area of the object?

The object described is made by attaching a triangle to a rectangle. To find the total area of the object, we need to calculate the areas of both the triangle and the rectangle separately and then sum them.

### Step 1: Area of the Triangle
The area \( A_{\text{triangle}} \) of a triangle is given by the formula:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, the base of the triangle is \( Z = 19 \) inches and the height \( H = 6 \) inches.

\[
A_{\text{triangle}} = \frac{1}{2} \times 19 \times 6 = \frac{1}{2} \times 114 = 57 \, \text{square inches}
\]

### Step 2: Area of the Rectangle
The area \( A_{\text{rectangle}} \) of a rectangle is given by the formula:
\[
A_{\text{rectangle}} = \text{base} \times \text{width}
\]
The base of the rectangle is \( C = 19 \) inches (since it shares a side with the triangle), and the width is \( W = 4 \) inches.

\[
A_{\text{rectangle}} = 19 \times 4 = 76 \, \text{square inches}
\]

### Step 3: Total Area of the Object
To find the total area of the object, sum the areas of the triangle and the rectangle:
\[
A_{\text{total}} = A_{\text{triangle}} + A_{\text{rectangle}} = 57 + 76 = 133 \, \text{square inches}
\]

Thus, the total area of the object is **133 square inches**.

Would you like a more detailed explanation, or do you have any other questions?

Here are 5 related questions to explore further:
1. How does the shape change if the base of the triangle is different from the side of the rectangle?
2. Can you calculate the perimeter of the combined shape?
3. What happens to the total area if the height of the triangle is doubled?
4. How would you calculate the area if the triangle was an isosceles triangle?
5. How does the area change if both the base and height of the rectangle are scaled by a factor?

**Tip**: Always double-check the measurements used in area formulas to ensure consistency in the calculation.

An image of object obtained by attaching a triangle with one side length z is attached to a rectangle with base C and width w. The other two sides of triangle are X, Y, and height H. If Y = 14 inches, Z = 19 inches, H = 6 inches, and W = 4 inches, what is the area of the object?

Learn how to calculate the area of a composite object made by attaching a triangle with base 19 inches and height 6 inches to a rectangle with base 19 inches and width 4 inches. This problem involves fundamental geometry concepts and is suitable for students in Grades 6-8.

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