The area of the shaded portion is equal to the area of the large triangle minus the combined area of the two smaller triangles.
To find the area of the large triangle, we need to find the length of its base and its height. Since the triangle is equilateral, the length of its base is equal to the width of the square, which is 5 inches.
To find the height of the triangle, we can use the Pythagorean theorem. The height is the hypotenuse of a right triangle with one side equal to half the length of the base (5/2 inches) and another side equal to the height of the square (also 5 inches).
Using the Pythagorean theorem:
height^2 = (5/2)^2 + 5^2
height^2 = 25/4 + 25
height^2 = 100/4 + 100/4
height^2 = 200/4
height^2 = 50
height = √50
The area of the large triangle is (1/2) * base * height = (1/2) * 5 * √50 = (5/2) * √50
To find the area of the two smaller triangles, we can divide the area of the large triangle by 2. Therefore, the area of each smaller triangle is (5/2) * √50 / 2 = (5/4) * √50
The total area of the shaded portion is then the area of the large triangle minus the combined area of the two smaller triangles:
(5/2) * √50 - 2 * (5/4) * √50 = (5/2) * √50 - (10/4) * √50 = (5/2 - 5/2) * √50 = 0 * √50 = 0
Therefore, the fashion designer does not need any red silk to make the scarf.
A fashion designer created a sketch of a square scarf. The design has one large triangle and two congruent smaller triangles. The shaded portion shows the part made from red silk. The sketch of the scarf has a scale of 5 inches = 3 feet. How much red silk does the fashion designer need to make the scarf?
An equilateral triangle within a square that is 5 inches wide. The base of the triangle is the same width as the square and the top of the triangle touches the top of the square.
CLEAR SUBMIT
2.25 ft2
2
.
25
ft
2
4.5 ft2
4
.
5
ft
2
6.25 ft2
6
.
25
ft
2
12.5 ft2
1 answer
1 answer