DSAT extra practice Ch5 Lv3

Mia has a circular pie with radius 8 inches. She wants to put a piece of large chocolate to decorate it. If the shape of the chocolate is a square, what is the maximum area, insquare inches, of the chocolate?

In the figure, [math]AEFD[/math] and [math]EBCF[/math] are rectangular. Which of the following values could be the area of triangle [math]BPC[/math]?

The figure shows three squares and a regular hexagon. If the area of the hexagon is [math]360\sqrt{3}[/math], what is summation of the areas of these three squares?

In the figure, [math]ABC[/math] is a right triangle. [math]D[/math] is on [math]\overline{BC}[/math] so that [math]\overline{AD}[/math] is perpendicular to [math]\overline{BC}[/math]. Which of the following values is closest to the length of [math]\overline{AD}[/math]?

In the figure, [math]ABCD[/math] is a trapezoid where [math]\overline{AD}[/math] is parallel to [math]\overline{BC}[/math]. Which of the following values is closest to the height of this trapezoid?

The figure shows a triangle [math]ABC[/math]. [math]O[/math] is inside the triangle that satisfies [math]OA=OB=OC[/math]. What is the summation of [math]m\angle OAB, m\angle OBC[/math], and [math]m\angle OCA[/math]?

In the figure, [math]ABC[/math] is a right triangle. [math]D[/math] and [math]E[/math] are on [math]\overline{AC}[/math] and [math]\overline{AB}[/math] respectively. If [math]m\angle ADE=40^\circ[/math] and [math]m\angle ACB=35^\circ[/math], which of the following statements about [math]\angle AED[/math] is true?

In the figure, [math]ABCD[/math] is a parallelogram. [math]F[/math] is the intersection of [math]\overline{AC}[/math] and [math]\overline{DE}[/math]. If the area of triangle [math]EFC[/math] is [math]k[/math] where [math]k[/math] is a positive constant, which of the following expressions is the area of [math]ABCD[/math]?

If [math]\tan\theta=\dfrac{1}{2}[/math], what is the area of triangle [math]ABC[/math]?

If [math]45^\circ<\theta<90^\circ[/math], which of the following values is smallest?

If [math]\tan\theta=1.5[/math], what is the length of [math]\overline{DE}[/math]?

Let [math]ABC[/math] be a triangle satisfying [math]AB=AC=4[/math]. If [math]\cos(\angle B)=\dfrac{1}{2}[/math], what is the area of [math]ABC[/math]?

Let [math]ABC[/math] be an isosceles triangle and [math]AB=AC=5[/math]. If [math]m\angle A=0.5[/math] radians, what is the length of [math]\overline{BC}[/math]?

In the figure, [math]OAB[/math] is a sector. If the length of [math]\overset{\frown}{AB}[/math] is [math]6[/math], what is the length of [math]\overline{OC}[/math]?

In the figure, [math]OAB[/math] is a sector. What is area of the shaded region?

Katrina uses a sector paper with radius 15 inches to form a cone. If the radius of the cone is 5 inches, what is the central angle, in radians, of the sector paper?

Circle [math]C: x^2+y^2=4[/math] and line [math]\ell:3x+4y=12[/math] are on the [math]xy[/math]-plane. If particles [math]P[/math] and [math]Q[/math] are moving on [math]\ell[/math] and [math]C[/math] respectively, what is the minimum of [math]PQ[/math]?

Let [math]C: (x-h)^2+(y-k)^2=r^2[/math] be a circle where [math]h, k[/math], and [math]r[/math] are constants. If two points [math]A(1,7)[/math] and [math]B(1,1)[/math] are on [math]C[/math], which of the following statements is incorrect?

Three circles [math]A, B[/math], and [math]C[/math] are tangent to each other. If the radii of these circles are 2, 4, and 6 respectively, what is the area of triangle [math]ABC[/math]?

If the area of triangle [math]ABE[/math] is [math]k[/math] where [math]k[/math] is a positive number, which of the following expression is the area of triangle [math]CDE[/math]?

The figure shows a sector with radius 15 and a rectangle. If the area of rectangle is 108, what is the perimeter of the rectangle?

In the figure, [math]ABCD[/math] is a rectangle. If [math]\cos\angle CAB=\dfrac{1}{3}[/math], what is the length of [math]\overline{EF}[/math]?