To find the height of the rectangle, we need to know the dimensions of the composite shape. Since the area of the drawing is given as 78 square centimeters, we need to find the length of the base (width) of the rectangle.
Let h be the height of the rectangle and b be the length of the rectangle.
The area of a rectangle is given by the formula A = l * w, where A is the area, l is the length, and w is the width.
In this case, the area is 78 square centimeters, so we have:
78 = h * b
Since the drawing is a composite shape, we can see that the drawing consists of a rectangle and a triangle of the same base (width). Since the height of the rectangle is equal to the height of the triangle, and the area of the triangle is half the area of the rectangle, we can write:
Area of rectangle = Area of triangle * 2
78 = (1/2) * h * b * 2
Solving the equation for h, we get:
78 = h * b
78 = (1/2) * h * b * 2
78 = h * b
78 = 2h * b (h is equal to b in this case)
78 = 2h^2
h^2 = 39
h = sqrt(39) ≈ 6.24
So, the height of the rectangle is approximately 6.24 cm.
None of the given options match the calculated value of the height.
John Roy creates this drawing of a composite shape for an art contest. The area of the drawing is 78 square centimeters. What is the height of the rectangle?
(1 point)
• 12cm
• 8cm
• 10cm
• 13cm
1 answer