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14 problems match “triangle area”. Clear

Area of a parallelogram on a log graph ●●●○○ 50 ptsGiven points $A(3,1)$ and $B\left(\frac{5}{3},2\right)$ . The four vertices of parallelogram $ABCD$ all lie on the graph of $f(x)=\log_{2}\frac{ax+b}{x-1}$ . Find the area of parallelogram $ABCD$ . Round to two decimal places.
Area ratio of faces in a pyramid ●●●○○ 50 ptsThe height of the triangular pyramid $ABCD$ , dropped from vertex $D$ , passes through the point of intersection of the heights of triangle $ABC$ . In addition, it is known that $DB=3$ , $DC=2$ , $\angle BDC=90^{\circ}$ . Find the ratio of the area of face $ADB$ to the area of face $ADC$ .
Area of triangle BDE in space ●●●○○ 50 ptsPoints $A$ , $B$ , $C$ , $D$ , and $E$ are located in 3-dimensional space with $AB= BC= CD= DE= EA= 2$ and $\angle ABC = \angle CDE = \angle DEA = 90^\circ$ . The plane of triangle $ABC$ is parallel to $\overline{DE}$ . What is the area of triangle $BDE$ ?
Side length of a square tilted to a plane ●●●●○ 100 ptsGiven a square $ABCD$ with side length $a$ , vertex $A$ lies in plane $\beta$ , and the other vertices are on the same side of plane $\beta$ . The distances from points $B$ and $D$ to plane $\beta$ are 1 and 2, respectively. If the angle between plane $ABCD$ and plane $\beta$ is $30^\circ$ , find $a$ . Round to two decimal places.