Question

use the following information to answer the next question. the window shown below consists of a rectangle and a semi - circle. 4. the area of the window, correct to one decimal place, is a. 1.8 m² b. 2.3 m² c. 1.5 m² d. 3.5 m² use the following information to answer the next question. a child’s toy is in a box that measures 2 units by 3 units by 6 units. 5. the surface area of the box is: a. 36 units² b. 64 units² c. 72 units² d. 96 units²

Explanation:

Step1: Calculate area of rectangle

The area formula for a rectangle is $A_{rect}=l\times w$. For the window, $l = 1.2$m and $w = 1.0$m, so $A_{rect}=1.2\times1.0 = 1.2$m².

Step2: Calculate area of semi - circle

The diameter of the semi - circle is $d = 1.2$m, so the radius $r=\frac{d}{2}=\frac{1.2}{2}=0.6$m. The area formula for a full - circle is $A=\pi r^{2}$, and for a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Substituting $r = 0.6$m, we get $A_{semicircle}=\frac{1}{2}\times\pi\times(0.6)^{2}=\frac{1}{2}\times\pi\times0.36\approx0.565$m².

Step3: Calculate total area of window

$A = A_{rect}+A_{semicircle}=1.2 + 0.565=1.765\approx1.8$m².

Step4: Calculate surface area of box

The box is a rectangular prism with length $l = 6$ units, width $w = 3$ units and height $h = 2$ units. The surface area formula for a rectangular prism is $SA=2(lw+lh+wh)$.
Substitute the values: $SA = 2(6\times3+6\times2+3\times2)=2(18 + 12+6)=2\times36 = 72$ units².

Answer:

1. A. $1.8$ m²
2. C. $72$ units²