Question

This blue shape is made of three quarters of a ring with a triangular arrowhead. Calculate the total area to three significant figures.

Answer 1

In an equilateral triangle, all the sides are the same length and all the angles are the same size. 60º. 60º. 60º. KEY WORD. Polygon a shape with three or more.

Explanation:

Answer 2

The total area of the blue shape is 148.47 cm²

The area of the blue shape can be calculated by dividing it into two parts: the area of the three-quarters ring and the area of the triangular arrowhead.

Area of the three-quarters ring:

• First, calculate the area of a whole ring. The formula for the area of a ring is
  `A_r_i_n_g` = πr₂² - πr₁², where r₂ is the outer radius and r₁ is the inner radius.
• In this case, the outer radius (r₂) is 15 cm and the inner radius (r₁) is 9 cm.
• Therefore, the area of the whole ring is
  `A_r_i_n_g` = π * 15² cm² - π * 9² cm² ≈ 176.63 cm²
• Since the blue shape is made of three-quarters of the ring, its area is 3/4 *
  `A_r_i_n_g` ≈ 132.47 cm²

Area of the triangular arrowhead:

The area of a triangle is calculated using the formula
`A_t_r_i_a_n_g_l_e` = 1/2 * base * height

In the image, the base of the triangle is 8 cm and the height is 4 cm.

Therefore, the area of the triangular arrowhead is
`A_t_r_i_a_n_g_l_e` = 1/2 * 8 cm * 4 cm = 16 cm²

Total area:

Finally, add the area of the three-quarters ring and the area of the triangular arrowhead to find the total area of the blue shape.

Total area ≈ 132.47 cm² + 16 cm² ≈ 148.47 cm²

Therefore, the total area of the blue shape is approximately 148.47 square centimeters, rounded to three significant figures.