A gift box is in the shape of a trapezoidal prism with base lengths of7 inches and 5 inches and a height of 4 inches. The height of the gift box is 8 inches. What is the volume of the gift box?

192 in³

Step-by-step explanation:

A trapezoidal prism is a three dimensional solid that has two similar trapezoids at its top and base.The two similar trapezoids are connected by four rectangles connecting the corresponding sides of the two bases.

The Area of the trapezoid at the top or base = 1/2 (a + b)h

Where a and b are the lengths =  7 inches and 5 inches and the height (h) = 4 inches.

Therefore Area of the trapezoid at the top or base = 1/2 (a + b)h = 1/2(7 + 5)4 = 24 in²

The volume of gift box = Area of the trapezoid at the top or base × height of gift box = 24 × 8 = 192 in³

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°